Combinations and Permutations

CHAPTER 4.4

Permutations are used when arranging r out of n items in a specific order.

nPr=

PERMUTATIONS

)!(

!

rn

n

The advertising director for a television show has 7 ads to use on the program. If she selects one of them for the opening of the show, one for the middle of the show, and one for the ending of the show, how many possible ways can this be accomplished?

TELEVISION ADS

A school musical director can select two musical plays to present next year. One will be presented in the fall, and one will be presented in the spring. If she has nine to pick from, how many different possibilities are there?

SCHOOL MUSICAL PLAYS

Combinations are used when the order or arrangement is not important

The formula for the number of combinations of r objects selected from n objects

nCr=

COMBINATIONS

!)!(

!

rrn

n

Given the letters A, B, C, and D, list the permutations and combinations for selecting two letters.

COMBINATIONS VS. PERMUTATIONS

How many combinations of 4 objects are there taken 2 at a time?

COMBINATIONS

A newspaper editor has received eight books to review. He decides that he can use three reviews in his newspaper. How many different ways can these three reviews be selected?

BOOK REVIEWS

In a club there are seven women and five men. A committee of three women and two men is to be chosen. How many different possibilities are there?

COMMITTEE SELECTION

The general manager of a fast-food restaurant chain must select six restaurants from eleven for a promotional program. How many different possible ways can this selection be done?

PROMOTIONAL PROGRAM

How many different tests can be made from a test bank of twenty questions if the test consists of five questions?

QUESTIONS FOR A TEST

There are sixteen seniors and fifteen juniors in a particular social organization. In how many ways can four seniors and two juniors be chosen to participate in a charity event?

CHARITY EVENT

Pg. 240 #1-7

APPLYING THE CONCEPTS