CHAPTER 4.4
Combinations
and
Permutations
PERMUTATIONS
 Permutations are used when arranging r out of n
items in a specific order.
nP r=
n!
(n  r )!
TELEVISION ADS
 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?
SCHOOL MUSICAL PLAYS
 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?
COMBINATIONS
 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
nC r=
n!
(n  r )! r!
COMBINATIONS VS. PERMUTATIONS
 Given the letters A, B, C, and D, list the permutations
and combinations for selecting two letters.
COMBINATIONS
 How many combinations of 4 objects are there taken
2 at a time?
BOOK REVIEWS
 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?
COMMITTEE SELECTION
 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?
PROMOTIONAL PROGRAM
 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?
QUESTIONS FOR A TEST
 How many different tests can be made from a test
bank of twenty questions if the test consists of five
questions?
CHARIT Y EVENT
 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?
APPLYING THE CONCEPTS
 Pg. 240 #1-7