Suppose that a department contains 10 men and 12 women. How many ways are there to form a committee with six members if it must have the sam

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Suppose that a department contains 10 men and 12 women. How many ways are there to form a committee with six members if it must have the same number of men and women

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Dâu 4 years 2021-08-05T17:21:02+00:00 1 Answers 506 views 0

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  1. Nho
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    2021-08-05T17:22:27+00:00
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    Answer:

    The number of ways is 26,400 ways

    Step-by-step explanation:

    Given;

    total number of men, M = 10

    total number of women, W = 12

    number of committees to be formed = 6

    If there must be equal gender, then it must consist of 3 men and 3 women.

    The \ number \ of \ ways = 10C_3 \times 12C_3\\\\The \ number \ of \ ways =\frac{10!}{3!7!} \times \frac{12!}{3!9!} \\\\T he \ number \ of \ ways = 120 \times 220 = 26,400 \ ways

    Therefore, the number of ways is 26,400 ways

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