题目
(a) Find the number of ways in which a committee of 6 people can be chosen from 6 men and 8 women if it must include 3 men and 3 women.
A different committee of 6 people is to be chosen from 6 men and 8 women. Three of the 6 men are brothers.
(b) Find the number of ways in which this committee can be chosen if there are no restrictions on the numbers of men and women, but it must include no more than two of the brothers.
题目中文翻译
(a) 从 6 名男性和 8 名女性中选出一个由 6 人组成的委员会，要求其中必须有 3 名男性和 3 名女性，求选取方式的种数。
现要从 6 名男性和 8 名女性中选出另一个由 6 人组成的委员会。这 6 名男性中有三人是兄弟。
(b) 若不限制委员会中男性和女性的人数，但这三兄弟中最多只能有两人入选，求选取该委员会的方式种数。
原卷通用作答要求
Answer all questions. You should use a calculator where appropriate.
You must show all necessary working clearly; no marks will be given for unsupported answers from a calculator.
Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.
请回答所有题目。适当时应使用计算器。必须清楚展示所有必要的计算过程；仅给出计算器答案而没有过程，不予评分。除非题目另有精度要求，非精确数值答案保留 3 位有效数字，以度为单位的角度保留 1 位小数。
解答
(a)
解法一
思路
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男女分别选三人，组合数相乘。
答题过程
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(b)
解法一
思路
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按三兄弟入选0、1、2人分类，另外11人不受性别人数限制。
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The permitted numbers of brothers are 0, 1 and 2. Thus
解法二
思路
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也可以从全部六人委员会中减去三兄弟全部入选的情况。
答题过程
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There are unrestricted committees. If all three brothers are included, the other three members are chosen from the remaining eleven. Hence