1. Section 12.10 Solving Probability Problems by Using Combinations

2. What You Will Learn
Using Combinations to Solve Probability Problems

3. Example 1: Committee of Three Women
A club consists of four men and five women. Three members are to be selected at random to form a committee. What is the probability that the committee will consist of three women?

4. Example 1: Committee of Three Women
Solution
Order is not important: combinations

5. Example 3: Employment Assignments
A temporary employment agency has six men and five women who wish to be assigned for the day. One employer has requested four employees for security guard positions, and the second employer has requested three employees for moving furniture in an office building.

6. Example 3: Employment Assignments
If we assume that each of the potential employees has the same chance of being selected and being assigned at random and that only seven employees will be assigned, find the probability that
a) three men will be selected for moving furniture.

7. Example 3: Employment Assignments
Solution

8. Example 3: Employment Assignments
b) three men will be selected for moving furniture and four women will be selected for security guard positions.

9. Example 3: Employment Assignments
Solution

10. Example 5: Rare Coins
Conner Shanahan’s rare coin collection is made up of 8 silver dollars, 7 quarters, and 5 dimes. Conner plans to sell 8 of his 20 coins to finance part of his college education. If he selects the coins at random, what is the probability that 3 silver dollars, 2 quarters, and 3 dimes are selected?

11. Example 5: Rare Coins
Solution