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Bunuel
The co-op board of a certain residential building must consist of two men and three women. If there are six men and seven women who want to be on the committee, how many different make-ups of the committee exist?

A. 65
B. 525
C. 1,050
D. 1,287
E. 100,800

6C2 x 7C3 = [(6 x 5) / 2] x [(7 x 6 x 5) / (3 x 2)] = 15 x 35 = 525

Answer: B
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Solution



Given
In this question, we are given that
    • The co-op board of a certain residential building must consist of two men and three women.
    • There are six men and seven women who want to be on the committee.

To find
We need to determine
    • The number of different committees that can exist

Approach and Working out
In the formation of the committee,
    • 2 men need to be chosen from 6 men in \(^6C_2\) or 15 ways
    • 3 women need to be chosen from 7 women in \(^7C_3\) or 35 ways

Hence, the number of ways the formation can be done = 15 x 35 = 525


Thus, option B is the correct answer.

Correct Answer: Option B
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