72 \ (2)(3) = 6 Pant 2 53 k n n n 1 2 k n n ... n n - - PowerPoint PPT Presentation

▶
72
SMART_READER_LITE
LIVE PREVIEW

72 \ (2)(3) = 6 Pant 2 53 k n n n 1 2 k n n ... n n - - PowerPoint PPT Presentation

Sep 29, 2022 516 likes •758 views

, ,Pz3 EP f- z shirts - pxSSILsnsz.Si3lpxsI-lPl.lslshirt1pant11shit2@P1.s 72 \ (2)(3) = 6 Pant 2 53 k n n n 1 2 k n n ... n n k 1 2 k 1 k we 22-52 26 ' 16 1600 5 . gb za = = - . 63 E I

slide-1
SLIDE 1
slide-2
SLIDE 2
slide-3
SLIDE 3 (2)(3) = 6 k n n n k n ⋅ n ⋅ ... ⋅ n ⋅ n 1 2 k 1 2 k−1 k f- EP , ,Pz3 pxSSILsnsz.Si3lpxsI-lPl.lslshirt1pant11shit2@P1.s z ✓
  • shirts
\

€72

Pant 2 53 we
slide-4
SLIDE 4 1600 = 16
  • 22-52
=

26

. 5 '

za

. gb a E E , I , 2 , .
  • 63

total

ways b e lo , I , 23 = f #
  • ptions for

2) ( #

  • f
  • ptions for 5)
=

( 6

t I ) ( 2 t I ) = 7 . 3=1217

proper

factors

: 2 I
  • 2
= 19
slide-5
SLIDE 5

3-63-6 EG

. . . .

I

=/3

slide-6
SLIDE 6 S M C ∣S ∪ M ∪ C∣ = ∣S∣ + ∣M∣ + ∣C∣ = 3 + 4 + 2 = 9 k n , n , ...n n + n + ... + n 1 2 k 1 2 k
slide-7
SLIDE 7 x 50 = 40 + 25 − x ⇒ x = 15

IA UBI =/

At tf BI
  • I
An BI TO 40 25
slide-8
SLIDE 8 Mutt
  • f
3 : 3
  • I
, 3 . 2 ,
  • 3
. 333 : 1333J malt
  • f
5 :

51,5-2

,
  • 5
  • 200
malt
  • f
15 :

15-1,15-2

, .
  • 15%6

:/

66J

Total

:

333+200-66=14677

slide-9
SLIDE 9

5-

I

  • 3-21
= 5 !

5-

I

  • 3
=

Go

473£

⇒ diff
slide-10
SLIDE 10 n! = n ⋅ (n − 1) ⋅ ... ⋅ 2 ⋅ 1 k n P(n, k) = 5 ⋅ 4 ⋅ 3 = = n n! P(n, n) = = n! (n − k)! n! 2⋅1 5⋅4⋅3⋅2⋅1 2! 5! 0! n!
  • i÷n
.
slide-11
SLIDE 11 3! = 6

D

RADI

Pilar

AD , Dz A Dz D , how many permutations
  • f
D , R : 2 !

DADD

:

RADAR

. .
  • .
. 3 !
slide-12
SLIDE 12 M : I 11 !

1111

: 4
  • ssss
: 4

(

4714114

'D

repeat PP : 2 repeated Tnepeasted Ps "
slide-13
SLIDE 13 BB 2 ! A Y How many times do the characters
  • f
DOG appear next to each
  • ther
, any
  • rder
:

I

: :

:* :

:

:O.

slide-14
SLIDE 14

,

÷

,
  • rotated
. but gray

;;t

5 !

I

=

4

!
slide-15
SLIDE 15 3! = 6 3! 3! = = 10 2! 5! 2! 5! 2!3! 5! 2 ⋅ 1 ⋅ 3! 5 ⋅ 4 ⋅ 3!
slide-16
SLIDE 16 k n = n k = k n − k {A, B, C, D, E} (k n) (n − k)!k! n! (k n) (n−k n ) C II
  • C 5)

( it

  • C : )
slide-17
SLIDE 17 (3 8) (5 9) (3 8)(5 9)

O

  • O

O

  • 00
slide-18
SLIDE 18 k 8 − k ways(at least 4 b) = ways(4 b) + ways(5 b) + ways(6 b) + ways(7 b) + ways(8 b) = + + + + (4 8)(4 9) (5 8)(3 9) (6 8)(2 9) (7 8)(1 9) (8 8)(0 9)
slide-19
SLIDE 19

I

13

. ( 42 ) .

(

I }) . 43
  • I

#÷¥÷

.

÷÷

I # ¥

.

Find

slide-20
SLIDE 20

EE

.

4¥

. '

EE

.

9.

4-4.4-4.4=19-457

  • g. I
Y I
  • 44k¥17
slide-21
SLIDE 21 It 2T . .
  • .
th = ( ntl ) S = I tht
  • th

combinatorial

S= nth
  • Ht
.
  • t
I

proof

  • Show
LHS and

ABCDE

( I)

KHS count
  • same

quantity

AB ,

AI.AD.AE

4

BE

, BD , BE 3 CD , CE 2 DE I
slide-22
SLIDE 22