Problem 7

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

 

 

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