Sect. 12-2 Permutations

Def: When a group of objects or people are arranged in a certain order, the arrangement is called a permutation.

1.Suppose a Theater owner has 11 films for an 8 screen theater. How many different arrangements are there for 8 screens to show 11 movies?

Def: The number of permutations of n objects taken r at a time is defined as

!!

,rn

nrnP

Where n! is factorial

2. Find 8!

3. (use formula) Suppose a Theater owner has 11 films for an 8 screen theater. How many different arrangements are there for 8 screens to show 11 movies?

4.A group of 5 friends went to a movie and found 7 empty seats. How many ways can they be seated?

5.How many ways can 2 math books, 4 geography books, 4 English books, 5 history and 3 physics books be arranged on a shelf?

Def: The number of permutations of n objects of which p are alike and q are alike is given by

!!

!

qp

n

!!

!

qp

n

6.How many ways can the letters of MISSISSIPPI be arranged?

Def: If n objects are arranged in a circle then the number of permutations is given by:

!1!nor

n

n

7.There are 4 people seated at a round table. How many arrangements are possible?

Reflections such as keys on a ring : there are half as many

Assignment: Page 723 # 14, 17, 20, 23, 25, 32, 33, 41, and 42