In how many ways can a group of 6 men and 3 women be made out of a total of 8…

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In how many ways can a group of 6 men and 3 women be made out of a total of 8 men and 5 women ?

  1. A.

    406

  2. B.

    154

  3. C.

    308

  4. D.

    280

Attempted by 8 students.

Show answer & explanation

Correct answer: D

Step-by-Step Solution

  1. Choose the men: We need to select 6 men out of 8. C(8, 6) = C(8, 2) = (8 * 7) / (2 * 1) = 28 ways.

  2. Choose the women: We need to select 3 women out of 5. C(5, 3) = C(5, 2) = (5 * 4) / (2 * 1) = 10 ways.

  3. Calculate the total combinations: Since these choices are independent, we multiply the number of ways to choose the men by the number of ways to choose the women. Total ways = 28 * 10 = 280.

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