March 12-14 ictcm.com | #ICTCM 32 nd International Conference on - - PowerPoint PPT Presentation

▶
march 12 14
SMART_READER_LITE
LIVE PREVIEW

March 12-14 ictcm.com | #ICTCM 32 nd International Conference on - - PowerPoint PPT Presentation

May 15, 2023 310 likes •942 views

32 nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL March 12-14 ictcm.com | #ICTCM 32 nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14 #ICTCM You Can Count on

slide-1
SLIDE 1

32nd International Conference on Technology in Collegiate Mathematics

ictcm.com | #ICTCM

ORLANDO, FL

March 12-14

slide-2
SLIDE 2

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM

You Can “Count” on Me!

A Counting Strategy for Undergraduates

slide-3
SLIDE 3

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM

  • Dr. Scott Demsky

Associate Professor Broward College Department of Mathematics Davie, Florida sdemsky@broward.edu

slide-4
SLIDE 4

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM

You Can “Count” on Me!

A Counting Strategy for Undergraduates

  • Students in Liberal Arts Math, Quantitative Reasoning or

Statistics often have difficulty counting the number of ways in which an event can occur.

slide-5
SLIDE 5

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM

You Can “Count” on Me!

A Counting Strategy for Undergraduates

  • Students in Liberal Arts Math, Quantitative Reasoning or

Statistics often have difficulty counting the number of ways in which an event can occur.

  • Should they use:

– The Fundamental Counting Principle?

slide-6
SLIDE 6

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM

You Can “Count” on Me!

A Counting Strategy for Undergraduates

  • Students in Liberal Arts Math, Quantitative Reasoning or

Statistics often have difficulty counting the number of ways in which an event can occur.

  • Should they use:

– The Fundamental Counting Principle? – Factorials or Permutations?

slide-7
SLIDE 7

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM

You Can “Count” on Me!

A Counting Strategy for Undergraduates

  • Students in Liberal Arts Math, Quantitative Reasoning or

Statistics often have difficulty counting the number of ways in which an event can occur.

  • Should they use:

– The Fundamental Counting Principle? – Factorials or Permutations? – Combinations?

slide-8
SLIDE 8

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM

You Can “Count” on Me!

A Counting Strategy for Undergraduates

  • Students in Liberal Arts Math, Quantitative Reasoning or

Statistics often have difficulty counting the number of ways in which an event can occur.

  • Should they use:

– The Fundamental Counting Principle? – Factorials or Permutations? – Combinations? – More than one of these?

slide-9
SLIDE 9

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM

You Can “Count” on Me!

A Counting Strategy for Undergraduates

  • Students in Liberal Arts Math, Quantitative Reasoning or

Statistics often have difficulty counting the number of ways in which an event can occur.

  • Should they use:

– The Fundamental Counting Principle? – Factorials or Permutations? – Combinations? – More than one of these?

  • We will see how the following one-page decision chart

can be used to help students learn how to “count” successfully.

slide-10
SLIDE 10

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM Are the objects you’re counting all the same type?

Use Fundamental Counting Principle

Are you putting the objects in

  • rder?

No

Are you arranging ALL the objects?

Use Combinations: nCr

No Yes

Use Factorial: n! Use Permutations: nPr

Yes No

w ways x ways y ways z ways

= w·x·y·z ways

Can you repeat a selection?

Yes Yes No

You Can “Count” on Me!

A Counting Strategy for Undergraduates

  • Dr. Scott H. Demsky

Department of Mathematics Broward College, Davie, Florida sdemsky@broward.edu

slide-11
SLIDE 11

Let’s try some examples!

slide-12
SLIDE 12

#ICTCM

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

Don has 5 pairs of shoes, 2 pairs of pants, and 3 shirts. If all items match, how many different outfits can he wear?

slide-13
SLIDE 13

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM Are the objects you’re counting all the same type?

Use Fundamental Counting Principle

Are you putting the objects in

  • rder?

No

Are you arranging ALL the objects?

Use Combinations: nCr

No Yes

Use Factorial: n! Use Permutations: nPr

Yes No

w ways x ways y ways z ways

= w·x·y·z ways

Can you repeat a selection?

Yes Yes No Don has 5 pairs of shoes, 2 pairs of pants, and 3 shirts. If all items match, how many different outfits can he wear?

slide-14
SLIDE 14

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM Are the objects you’re counting all the same type?

Use Fundamental Counting Principle

Are you putting the objects in

  • rder?

No

Are you arranging ALL the objects?

Use Combinations: nCr

No Yes

Use Factorial: n! Use Permutations: nPr

Yes No

w ways x ways y ways z ways

= w·x·y·z ways

Can you repeat a selection?

Yes Yes No Don has 5 pairs of shoes, 2 pairs of pants, and 3 shirts. If all items match, how many different outfits can he wear?

slide-15
SLIDE 15

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM Are the objects you’re counting all the same type?

Use Fundamental Counting Principle

Are you putting the objects in

  • rder?

No

Are you arranging ALL the objects?

Use Combinations: nCr

No Yes

Use Factorial: n! Use Permutations: nPr

Yes No

w ways x ways y ways z ways

= w·x·y·z ways

Can you repeat a selection?

Yes Yes No Don has 5 pairs of shoes, 2 pairs of pants, and 3 shirts. If all items match, how many different outfits can he wear?

5 ∙ 2 ∙ 3 = 30

slide-16
SLIDE 16

#ICTCM

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

A multiple-choice test has 6 questions, each with 4 possible answers. How many ways are there to mark the answers?

slide-17
SLIDE 17

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM Are the objects you’re counting all the same type?

Use Fundamental Counting Principle

Are you putting the objects in

  • rder?

No

Are you arranging ALL the objects?

Use Combinations: nCr

No Yes

Use Factorial: n! Use Permutations: nPr

Yes No

w ways x ways y ways z ways

= w·x·y·z ways

Can you repeat a selection?

Yes Yes No A multiple-choice test has 6 questions, each with 4 possible

  • answers. How many ways are there to mark the answers?
slide-18
SLIDE 18

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM Are the objects you’re counting all the same type?

Use Fundamental Counting Principle

Are you putting the objects in

  • rder?

No

Are you arranging ALL the objects?

Use Combinations: nCr

No Yes

Use Factorial: n! Use Permutations: nPr

Yes No

w ways x ways y ways z ways

= w·x·y·z ways

Can you repeat a selection?

Yes Yes No A multiple-choice test has 6 questions, each with 4 possible

  • answers. How many ways are there to mark the answers?
slide-19
SLIDE 19

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM Are the objects you’re counting all the same type?

Use Fundamental Counting Principle

Are you putting the objects in

  • rder?

No

Are you arranging ALL the objects?

Use Combinations: nCr

No Yes

Use Factorial: n! Use Permutations: nPr

Yes No

w ways x ways y ways z ways

= w·x·y·z ways

Can you repeat a selection?

Yes Yes No A multiple-choice test has 6 questions, each with 4 possible

  • answers. How many ways are there to mark the answers?
slide-20
SLIDE 20

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM Are the objects you’re counting all the same type?

Use Fundamental Counting Principle

Are you putting the objects in

  • rder?

No

Are you arranging ALL the objects?

Use Combinations: nCr

No Yes

Use Factorial: n! Use Permutations: nPr

Yes No

w ways x ways y ways z ways

= w·x·y·z ways

Can you repeat a selection?

Yes Yes No A multiple-choice test has 6 questions, each with 4 possible

  • answers. How many ways are there to mark the answers?

4 ∙ 4 ∙ 4 ∙ 4 ∙ 4 ∙ 4

slide-21
SLIDE 21

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM Are the objects you’re counting all the same type?

Use Fundamental Counting Principle

Are you putting the objects in

  • rder?

No

Are you arranging ALL the objects?

Use Combinations: nCr

No Yes

Use Factorial: n! Use Permutations: nPr

Yes No

w ways x ways y ways z ways

= w·x·y·z ways

Can you repeat a selection?

Yes Yes No A multiple-choice test has 6 questions, each with 4 possible

  • answers. How many ways are there to mark the answers?

4 ∙ 4 ∙ 4 ∙ 4 ∙ 4 ∙ 4 = 46 = 4,096

slide-22
SLIDE 22

#ICTCM

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

In how many ways can you line up 6 people for a photograph?

slide-23
SLIDE 23

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM Are the objects you’re counting all the same type?

Use Fundamental Counting Principle

Are you putting the objects in

  • rder?

No

Are you arranging ALL the objects?

Use Combinations: nCr

No Yes

Use Factorial: n! Use Permutations: nPr

Yes No

w ways x ways y ways z ways

= w·x·y·z ways

Can you repeat a selection?

Yes Yes No In how many ways can you line up 6 people for a photograph?

slide-24
SLIDE 24

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM Are the objects you’re counting all the same type?

Use Fundamental Counting Principle

Are you putting the objects in

  • rder?

No

Are you arranging ALL the objects?

Use Combinations: nCr

No Yes

Use Factorial: n! Use Permutations: nPr

Yes No

w ways x ways y ways z ways

= w·x·y·z ways

Can you repeat a selection?

Yes Yes No In how many ways can you line up 6 people for a photograph?

slide-25
SLIDE 25

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM Are the objects you’re counting all the same type?

Use Fundamental Counting Principle

Are you putting the objects in

  • rder?

No

Are you arranging ALL the objects?

Use Combinations: nCr

No Yes

Use Factorial: n! Use Permutations: nPr

Yes No

w ways x ways y ways z ways

= w·x·y·z ways

Can you repeat a selection?

Yes Yes No In how many ways can you line up 6 people for a photograph?

slide-26
SLIDE 26

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM Are the objects you’re counting all the same type?

Use Fundamental Counting Principle

Are you putting the objects in

  • rder?

No

Are you arranging ALL the objects?

Use Combinations: nCr

No Yes

Use Factorial: n! Use Permutations: nPr

Yes No

w ways x ways y ways z ways

= w·x·y·z ways

Can you repeat a selection?

Yes Yes No In how many ways can you line up 6 people for a photograph?

slide-27
SLIDE 27

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM Are the objects you’re counting all the same type?

Use Fundamental Counting Principle

Are you putting the objects in

  • rder?

No

Are you arranging ALL the objects?

Use Combinations: nCr

No Yes

Use Factorial: n! Use Permutations: nPr

Yes No

w ways x ways y ways z ways

= w·x·y·z ways

Can you repeat a selection?

Yes Yes No In how many ways can you line up 6 people for a photograph?

slide-28
SLIDE 28

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM Are the objects you’re counting all the same type?

Use Fundamental Counting Principle

Are you putting the objects in

  • rder?

No

Are you arranging ALL the objects?

Use Combinations: nCr

No Yes

Use Factorial: n! Use Permutations: nPr

Yes No

w ways x ways y ways z ways

= w·x·y·z ways

Can you repeat a selection?

Yes Yes No In how many ways can you line up 6 people for a photograph?

6! = 720

slide-29
SLIDE 29

#ICTCM

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

To win the top prize in the Florida Fantasy 5 lottery, you must correctly select 5 different numbers from 1-36 (order doesn’t matter). How many selections are possible?

slide-30
SLIDE 30

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM Are the objects you’re counting all the same type?

Use Fundamental Counting Principle

Are you putting the objects in

  • rder?

No

Are you arranging ALL the objects?

Use Combinations: nCr

No Yes

Use Factorial: n! Use Permutations: nPr

Yes No

w ways x ways y ways z ways

= w·x·y·z ways

Can you repeat a selection?

Yes Yes No To win the top prize in the Florida Fantasy 5 lottery, you must correctly select 5 different numbers from 1-36 (order doesn’t matter). How many selections are possible?

slide-31
SLIDE 31

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM Are the objects you’re counting all the same type?

Use Fundamental Counting Principle

Are you putting the objects in

  • rder?

No

Are you arranging ALL the objects?

Use Combinations: nCr

No Yes

Use Factorial: n! Use Permutations: nPr

Yes No

w ways x ways y ways z ways

= w·x·y·z ways

Can you repeat a selection?

Yes Yes No To win the top prize in the Florida Fantasy 5 lottery, you must correctly select 5 different numbers from 1-36 (order doesn’t matter). How many selections are possible?

slide-32
SLIDE 32

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM Are the objects you’re counting all the same type?

Use Fundamental Counting Principle

Are you putting the objects in

  • rder?

No

Are you arranging ALL the objects?

Use Combinations: nCr

No Yes

Use Factorial: n! Use Permutations: nPr

Yes No

w ways x ways y ways z ways

= w·x·y·z ways

Can you repeat a selection?

Yes Yes No To win the top prize in the Florida Fantasy 5 lottery, you must correctly select 5 different numbers from 1-36 (order doesn’t matter). How many selections are possible?

slide-33
SLIDE 33

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM Are the objects you’re counting all the same type?

Use Fundamental Counting Principle

Are you putting the objects in

  • rder?

No

Are you arranging ALL the objects?

Use Combinations: nCr

No Yes

Use Factorial: n! Use Permutations: nPr

Yes No

w ways x ways y ways z ways

= w·x·y·z ways

Can you repeat a selection?

Yes Yes No To win the top prize in the Florida Fantasy 5 lottery, you must correctly select 5 different numbers from 1-36 (order doesn’t matter). How many selections are possible?

slide-34
SLIDE 34

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM Are the objects you’re counting all the same type?

Use Fundamental Counting Principle

Are you putting the objects in

  • rder?

No

Are you arranging ALL the objects?

Use Combinations: nCr

No Yes

Use Factorial: n! Use Permutations: nPr

Yes No

w ways x ways y ways z ways

= w·x·y·z ways

Can you repeat a selection?

Yes Yes No To win the top prize in the Florida Fantasy 5 lottery, you must correctly select 5 different numbers from 1-36 (order doesn’t matter). How many selections are possible? 36C5 = 376,992

slide-35
SLIDE 35

#ICTCM

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

In a race with 8 cars, in how many ways can the cars finish 1st place, 2nd place, and 3rd place? Assume no ties.

slide-36
SLIDE 36

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM Are the objects you’re counting all the same type?

Use Fundamental Counting Principle

Are you putting the objects in

  • rder?

No

Are you arranging ALL the objects?

Use Combinations: nCr

No Yes

Use Factorial: n! Use Permutations: nPr

Yes No

w ways x ways y ways z ways

= w·x·y·z ways

Can you repeat a selection?

Yes Yes No In a race with 8 cars, in how many ways can the cars finish 1st place, 2nd place, and 3rd place? Assume no ties.

slide-37
SLIDE 37

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM Are the objects you’re counting all the same type?

Use Fundamental Counting Principle

Are you putting the objects in

  • rder?

No

Are you arranging ALL the objects?

Use Combinations: nCr

No Yes

Use Factorial: n! Use Permutations: nPr

Yes No

w ways x ways y ways z ways

= w·x·y·z ways

Can you repeat a selection?

Yes Yes No In a race with 8 cars, in how many ways can the cars finish 1st place, 2nd place, and 3rd place? Assume no ties.

slide-38
SLIDE 38

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM Are the objects you’re counting all the same type?

Use Fundamental Counting Principle

Are you putting the objects in

  • rder?

No

Are you arranging ALL the objects?

Use Combinations: nCr

No Yes

Use Factorial: n! Use Permutations: nPr

Yes No

w ways x ways y ways z ways

= w·x·y·z ways

Can you repeat a selection?

Yes Yes No In a race with 8 cars, in how many ways can the cars finish 1st place, 2nd place, and 3rd place? Assume no ties.

slide-39
SLIDE 39

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM Are the objects you’re counting all the same type?

Use Fundamental Counting Principle

Are you putting the objects in

  • rder?

No

Are you arranging ALL the objects?

Use Combinations: nCr

No Yes

Use Factorial: n! Use Permutations: nPr

Yes No

w ways x ways y ways z ways

= w·x·y·z ways

Can you repeat a selection?

Yes Yes No In a race with 8 cars, in how many ways can the cars finish 1st place, 2nd place, and 3rd place? Assume no ties.

slide-40
SLIDE 40

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM Are the objects you’re counting all the same type?

Use Fundamental Counting Principle

Are you putting the objects in

  • rder?

No

Are you arranging ALL the objects?

Use Combinations: nCr

No Yes

Use Factorial: n! Use Permutations: nPr

Yes No

w ways x ways y ways z ways

= w·x·y·z ways

Can you repeat a selection?

Yes Yes No In a race with 8 cars, in how many ways can the cars finish 1st place, 2nd place, and 3rd place? Assume no ties.

slide-41
SLIDE 41

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM Are the objects you’re counting all the same type?

Use Fundamental Counting Principle

Are you putting the objects in

  • rder?

No

Are you arranging ALL the objects?

Use Combinations: nCr

No Yes

Use Factorial: n! Use Permutations: nPr

Yes No

w ways x ways y ways z ways

= w·x·y·z ways

Can you repeat a selection?

Yes Yes No In a race with 8 cars, in how many ways can the cars finish 1st place, 2nd place, and 3rd place? Assume no ties.

8P3 = 336

slide-42
SLIDE 42

#ICTCM

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

In a certain state, license plates are 3 letters followed by 3 numbers with no repetitions in either group. How many different license plates are there?

slide-43
SLIDE 43

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM Are the objects you’re counting all the same type?

Use Fundamental Counting Principle

Are you putting the objects in

  • rder?

No

Are you arranging ALL the objects?

Use Combinations: nCr

No Yes

Use Factorial: n! Use Permutations: nPr

Yes No

w ways x ways y ways z ways

= w·x·y·z ways

Can you repeat a selection?

Yes Yes No In a certain state, license plates are 3 letters followed by 3 numbers with no repetitions in either

  • group. How many different license plates are there?
slide-44
SLIDE 44

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM Are the objects you’re counting all the same type?

Use Fundamental Counting Principle

Are you putting the objects in

  • rder?

No

Are you arranging ALL the objects?

Use Combinations: nCr

No Yes

Use Factorial: n! Use Permutations: nPr

Yes No

w ways x ways y ways z ways

= w·x·y·z ways

Can you repeat a selection?

Yes Yes No In a certain state, license plates are 3 letters followed by 3 numbers with no repetitions in either

  • group. How many different license plates are there?
slide-45
SLIDE 45

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM Are the objects you’re counting all the same type?

Use Fundamental Counting Principle

Are you putting the objects in

  • rder?

No

Are you arranging ALL the objects?

Use Combinations: nCr

No Yes

Use Factorial: n! Use Permutations: nPr

Yes No

w ways x ways y ways z ways

= w·x·y·z ways

Can you repeat a selection?

Yes Yes No In a certain state, license plates are 3 letters followed by 3 numbers with no repetitions in either

  • group. How many different license plates are there?

# ways to arrange 3 different letters # ways to arrange 3 different numbers

∙

slide-46
SLIDE 46

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM Are the objects you’re counting all the same type?

Use Fundamental Counting Principle

Are you putting the objects in

  • rder?

No

Are you arranging ALL the objects?

Use Combinations: nCr

No Yes

Use Factorial: n! Use Permutations: nPr

Yes No

w ways x ways y ways z ways

= w·x·y·z ways

Can you repeat a selection?

Yes Yes No In a certain state, license plates are 3 letters followed by 3 numbers with no repetitions in either

  • group. How many different license plates are there?

# ways to arrange 3 different letters # ways to arrange 3 different numbers

∙

slide-47
SLIDE 47

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM Are the objects you’re counting all the same type?

Use Fundamental Counting Principle

Are you putting the objects in

  • rder?

No

Are you arranging ALL the objects?

Use Combinations: nCr

No Yes

Use Factorial: n! Use Permutations: nPr

Yes No

w ways x ways y ways z ways

= w·x·y·z ways

Can you repeat a selection?

Yes Yes No In a certain state, license plates are 3 letters followed by 3 numbers with no repetitions in either

  • group. How many different license plates are there?

# ways to arrange 3 different letters # ways to arrange 3 different numbers

∙

slide-48
SLIDE 48

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM Are the objects you’re counting all the same type?

Use Fundamental Counting Principle

Are you putting the objects in

  • rder?

No

Are you arranging ALL the objects?

Use Combinations: nCr

No Yes

Use Factorial: n! Use Permutations: nPr

Yes No

w ways x ways y ways z ways

= w·x·y·z ways

Can you repeat a selection?

Yes Yes No In a certain state, license plates are 3 letters followed by 3 numbers with no repetitions in either

  • group. How many different license plates are there?

# ways to arrange 3 different letters # ways to arrange 3 different numbers

∙

slide-49
SLIDE 49

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM Are the objects you’re counting all the same type?

Use Fundamental Counting Principle

Are you putting the objects in

  • rder?

No

Are you arranging ALL the objects?

Use Combinations: nCr

No Yes

Use Factorial: n! Use Permutations: nPr

Yes No

w ways x ways y ways z ways

= w·x·y·z ways

Can you repeat a selection?

Yes Yes No In a certain state, license plates are 3 letters followed by 3 numbers with no repetitions in either

  • group. How many different license plates are there?

# ways to arrange 3 different letters # ways to arrange 3 different numbers

∙

slide-50
SLIDE 50

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM Are the objects you’re counting all the same type?

Use Fundamental Counting Principle

Are you putting the objects in

  • rder?

No

Are you arranging ALL the objects?

Use Combinations: nCr

No Yes

Use Factorial: n! Use Permutations: nPr

Yes No

w ways x ways y ways z ways

= w·x·y·z ways

Can you repeat a selection?

Yes Yes No In a certain state, license plates are 3 letters followed by 3 numbers with no repetitions in either

  • group. How many different license plates are there?

# ways to arrange 3 different letters # ways to arrange 3 different numbers

∙

slide-51
SLIDE 51

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM Are the objects you’re counting all the same type?

Use Fundamental Counting Principle

Are you putting the objects in

  • rder?

No

Are you arranging ALL the objects?

Use Combinations: nCr

No Yes

Use Factorial: n! Use Permutations: nPr

Yes No

w ways x ways y ways z ways

= w·x·y·z ways

Can you repeat a selection?

Yes Yes No In a certain state, license plates are 3 letters followed by 3 numbers with no repetitions in either

  • group. How many different license plates are there?

26 26P3

# ways to arrange 3 different numbers

∙

slide-52
SLIDE 52

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM Are the objects you’re counting all the same type?

Use Fundamental Counting Principle

Are you putting the objects in

  • rder?

No

Are you arranging ALL the objects?

Use Combinations: nCr

No Yes

Use Factorial: n! Use Permutations: nPr

Yes No

w ways x ways y ways z ways

= w·x·y·z ways

Can you repeat a selection?

Yes Yes No In a certain state, license plates are 3 letters followed by 3 numbers with no repetitions in either

  • group. How many different license plates are there?

26 26P3

# ways to arrange 3 different numbers

∙

slide-53
SLIDE 53

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM Are the objects you’re counting all the same type?

Use Fundamental Counting Principle

Are you putting the objects in

  • rder?

No

Are you arranging ALL the objects?

Use Combinations: nCr

No Yes

Use Factorial: n! Use Permutations: nPr

Yes No

w ways x ways y ways z ways

= w·x·y·z ways

Can you repeat a selection?

Yes Yes No In a certain state, license plates are 3 letters followed by 3 numbers with no repetitions in either

  • group. How many different license plates are there?

26 26P3

# ways to arrange 3 different numbers

∙

slide-54
SLIDE 54

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM Are the objects you’re counting all the same type?

Use Fundamental Counting Principle

Are you putting the objects in

  • rder?

No

Are you arranging ALL the objects?

Use Combinations: nCr

No Yes

Use Factorial: n! Use Permutations: nPr

Yes No

w ways x ways y ways z ways

= w·x·y·z ways

Can you repeat a selection?

Yes Yes No In a certain state, license plates are 3 letters followed by 3 numbers with no repetitions in either

  • group. How many different license plates are there?

26 26P3

# ways to arrange 3 different numbers

∙

slide-55
SLIDE 55

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM Are the objects you’re counting all the same type?

Use Fundamental Counting Principle

Are you putting the objects in

  • rder?

No

Are you arranging ALL the objects?

Use Combinations: nCr

No Yes

Use Factorial: n! Use Permutations: nPr

Yes No

w ways x ways y ways z ways

= w·x·y·z ways

Can you repeat a selection?

Yes Yes No In a certain state, license plates are 3 letters followed by 3 numbers with no repetitions in either

  • group. How many different license plates are there?

26 26P3

# ways to arrange 3 different numbers

∙

slide-56
SLIDE 56

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM Are the objects you’re counting all the same type?

Use Fundamental Counting Principle

Are you putting the objects in

  • rder?

No

Are you arranging ALL the objects?

Use Combinations: nCr

No Yes

Use Factorial: n! Use Permutations: nPr

Yes No

w ways x ways y ways z ways

= w·x·y·z ways

Can you repeat a selection?

Yes Yes No In a certain state, license plates are 3 letters followed by 3 numbers with no repetitions in either

  • group. How many different license plates are there?

26 26P3

# ways to arrange 3 different numbers

∙

slide-57
SLIDE 57

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM Are the objects you’re counting all the same type?

Use Fundamental Counting Principle

Are you putting the objects in

  • rder?

No

Are you arranging ALL the objects?

Use Combinations: nCr

No Yes

Use Factorial: n! Use Permutations: nPr

Yes No

w ways x ways y ways z ways

= w·x·y·z ways

Can you repeat a selection?

Yes Yes No In a certain state, license plates are 3 letters followed by 3 numbers with no repetitions in either

  • group. How many different license plates are there?

26 26P3 10 10P3

∙

slide-58
SLIDE 58

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM Are the objects you’re counting all the same type?

Use Fundamental Counting Principle

Are you putting the objects in

  • rder?

No

Are you arranging ALL the objects?

Use Combinations: nCr

No Yes

Use Factorial: n! Use Permutations: nPr

Yes No

w ways x ways y ways z ways

= w·x·y·z ways

Can you repeat a selection?

Yes Yes No In a certain state, license plates are 3 letters followed by 3 numbers with no repetitions in either

  • group. How many different license plates are there?

11,232,000

slide-59
SLIDE 59

Thank you for your attendance!

slide-60
SLIDE 60

32nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14

#ICTCM Are the objects you’re counting all the same type?

Use Fundamental Counting Principle

Are you putting the objects in

  • rder?

No

Are you arranging ALL the objects?

Use Combinations: nCr

No Yes

Use Factorial: n! Use Permutations: nPr

Yes No

w ways x ways y ways z ways

= w·x·y·z ways

Can you repeat a selection?

Yes Yes No

You Can “Count” on Me!

A Counting Strategy for Undergraduates

  • Dr. Scott H. Demsky

Department of Mathematics Broward College, Davie, Florida sdemsky@broward.edu

slide-61
SLIDE 61