Suppose that a department contains 11 men and 15 women. How many ways are there to form a committee wit?

2016-06-13 4:31 am

(1 pt) Suppose that a department contains 11 men and 15 women. How many ways are there to form a committee with 6 members if it must have strictly more women than men?

回答 (2)

fooks

2016-06-13 4:40 am

Case 1 : It is NOT allowed that the committee has no man.

The committee should have (4 women, 2 men) or (5 women, 1 men).

Number of ways to form the committee
= C(15,4) × C(11,2) + C(15,5) × C(11,1)
= 1365 × 55 + 3003 × 11
= 108108

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Case 2 : It is ALLOWED that the committee has no man.

The committee should have (4 women, 2 men), (5 women, 1 men) or (6 women).

Number of ways to form the committee
= C(15,4) × C(11,2) + C(15,5) × C(11,1) + C(15,6)
= 1365 × 55 + 3003 × 11 + 5005
= 113113

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用戶57802

2016-06-13 4:33 am

4W2M or 5W1M or 6W
-->answer = 664510 ways

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