SOLUTION: A five-member committee is to be selected from among four representatives of management and five representatives of Labor. In how many different ways can the committee be formed un

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Question 1138095: A five-member committee is to be selected from among four representatives of management and five representatives of Labor. In how many different ways can the committee be formed under the following circumstances?
A. Anyone is eligible to serve on the committee?
B. The committee must consist of three representatives of management and two representatives of labor
C. The committee must consist of two representatives of management and three representatives of labor
D. The committee must contain at least three representatives of management
Answer by VFBundy(438) About Me  (Show Source):
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A. Anyone is eligible to serve on the committee?

9C5 = %289%21%2F%285%21%2A4%21%29%29 = 126

B. The committee must consist of three representatives of management and two representatives of labor

4C3 * 5C2 = %284%21%2F%283%21%2A1%21%29%29%2A%285%21%2F%282%21%2A3%21%29%29 = 40

C. The committee must consist of two representatives of management and three representatives of labor

4C2 * 5C3 = %284%21%2F%282%21%2A2%21%29%29%2A%285%21%2F%283%21%2A2%21%29%29 = 60

D. The committee must contain at least three representatives of management

(4C3 * 5C2) + (4C4 * 5C1) = %284%21%2F%283%21%2A1%21%29%29%2A%285%21%2F%282%21%2A3%21%29%29 + %284%21%2F%284%21%2A0%21%29%29%2A%285%21%2F%281%21%2A4%21%29%29 = 40 + 5 = 45