Counting Permutations - PowerPoint Presentation

Slide1

Counting Permutationswith Repetitions

ICS 6D

Sandy

IraniSlide2

Permutation Counting

How many ways to permute the letters in the word “BAD”?

BAD

BDA

ABD

ADB

DAB

DBASlide3

Permutation Counting

How many ways to permute the letters in the word “ADD”?

ADD

DAD

DDASlide4

Permutations with Repetitions

How many ways to permute the letters in the word “MISSISSIPPI”?

11 letters total

4 I’s

4 S’s

2 P’s

1 MSlide5

Permutations with RepetitionsGeneral Example

How many permutations are there of:

r

1

copes of c

1

r

2

copes of

c

2

…

r

k-1

copes of

c

k-1

r

k

copes of

c

k

r

1

+ r

2

+…+ r

k-1

+

r

k

= nSlide6

Permutations with RepetitionsGeneral Example

The number of permutations of:

r

1

copes of c

1

r

2

copes of

c

2…rk-1 copes of ck-1rk copes of ckr1 + r2 +…+ rk-1 + rk = n

 Slide7

Counting Permutations with Repetitions

How many strings over {a, b, c, d} have

6 a’s

3 b’s

2 c’s

7 d’sSlide8

Counting Permutations with Repetitions

How many ways to assign 20 different tasks to five distinct processors such that each processor gets the same number of tasks?Slide9

The number of ways to assign 20 distinct jobs to 5 distinct processors such that each processor gets 4 jobs

The number of sequences of length 20 with

Four 1’s

Four 2’s

Four 3’s

Four 4’s

Four 5’s=Slide10

Counting Permutations with Repetitions

How many ways to distribute cookies to 10 kids such that each kid gets one cookie? There are:

3 chocolate chip

1 sugar

4 ginger

2 oatmeal raisin

(Cookies of the same variety are identical)