Page 115 - Probability Demystified

104 CHAPTER 6 The Counting Rules

EXAMPLE: In a classroom, there are 8 women and 5 men. A committee of
3 women and 2 men is to be formed for a project. How many different
possibilities are there?

SOLUTION:
In this case, you must select 3 women from 8 women and 2 men from
5 men. Since the word ‘‘and’’ is used, multiply the answers.
8! 5!
C C ¼
8 3 5 2
ð8 3Þ!3! ð5 2Þ!2!
8! 5!
¼
5! 3! 3! 2!
8 7 6 5! 5 4 3!
¼ ¼ 56 10
5! 3 2 1 3! 2 1
¼ 560
Hence, there are 560 different ways to make the selection.

PRACTICE

1. In how many ways can a large retail store select 3 sites on which to
build a new store if it has 12 sites to choose from?
2. In how many ways can Mary select two friends to go to a movie with
if she has 7 friends to choose from?
3. In how many ways can a real estate agent select 10 properties to place
in an advertisement if she has 15 listings to choose from?
4. In how many ways can a committee of 3 elementary school teachers
be selected from a school district which has 8 elementary school
teachers?
5. In a box of 10 calculators, one is defective. In how many ways
can four calculators be selected if the defective calculator is included
in the group?