Combinations and Permutations

1
Chapter 4.4

• Combinations and Permutations

2
Permutations

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

3
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?

4
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?

5
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
• nCr

6
Combinations vs. permutations

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

7
combinations

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

8
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?

9
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?

10
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?

11
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?

12
Charity 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?

13
Applying the concepts

• Pg. 240 1-7