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)
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
====
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
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
====
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
2016-06-13 4:33 am
4W2M or 5W1M or 6W
-->answer = 664510 ways
-->answer = 664510 ways
收錄日期: 2021-04-18 15:05:33
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