Ten women and ten men are on the faculty in the mathematics department
at a school.
- How many ways are there to select a committee of five members of the
department if at least one woman must be on the committee?
1. We find the number of ways to select any 5 people, regardless of gender.
2. We find the number of ways to select 5 men.
3. We subtract the result of 2 from the result of 1.
1. That's C(20,5)
2. That's C(10,5)
3. That's C(20,5)-C(10,5) = 15504-252 = 15252
- How many ways are there to select a committee of five members of the
department if at least one woman and at least one man must be on the committee?
1. We find the number of ways to select any 5 people, regardless of gender.
2. We find the number of ways to select 5 men.
3. We find the number of ways to select 5 women.
4. We subtract the result of 2 and the result of 3 from the result of 1.
1. That's C(20,5)
2. That's C(10,5)
3. That's C(10,5)
4. That's C(20,5)-C(10,5)-C(10,5) = 15504-252-252 = 15000.
Edwin
