Problem – 7
Nine women and five men are on the faculty in the mathematics department at a school.
a) How many ways are there to select a committee of four members of the department if at least one woman must be on the committee?
b) How many ways are there to select a committee of four members of the department if at least one woman and at least one man must be on the committee?
Solution:
a) Number of ways to choose the four members if at least one woman must be on the committee = 9C1x5C3 + 9C2x5C2 + 9C3x5C1 + 9C4x5C0 = 90 + 360 + 420 + 126 = 996 ways
b) Number of ways to choose the four members if at least one woman and at least one man must be on the committee = 9C1x5C3 + 9C2x5C2 + 9C3x5C1 = 90 + 360 + 420 = 870 ways