一个读书俱乐部有 6 名男性和 8 名女性。该俱乐部的委员会由其中 5 名成员组成。Lan 先生和 Lan 太太都是俱乐部成员。

(a) 如果 Lan 先生和 Lan 太太中必须恰有一人入选委员会，有多少种不同的选法？

(b) 如果 Lan 太太必须入选委员会，且委员会中的女性人数必须多于男性人数，有多少种不同的选法？

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。

先选夫妻中哪一人入选，再从剩余12人中选4人。

Choose which one of Mr and Mrs Lan is included in 2 ways, then choose four of the other twelve members. Thus

也可从全部五人委员会减去夫妻均入选和夫妻均不入选两类。

There are $\binom{14}{5}$ unrestricted committees. Committees containing both Mr and Mrs Lan number $\binom{12}{3}$, and those containing neither number $\binom{12}{5}$. Hence

固定Lan太太后剩7女6男，另选四人时需要至少两女，分2、3、4女三类。

Include Mrs Lan. Among the remaining seven women and six men, choose the other four members as follows:

Thus