某俱乐部有 15 名成员，包括 6 名男性和 9 名女性。每周五随机选出 5 名成员组成一支队伍，代表俱乐部参加比赛。

(a) 求下周五所选队伍中男性人数多于女性人数的概率。

另一个俱乐部有 13 名成员。

(b) 将这 13 名成员分成一个 6 人组、一个 4 人组和一个 3 人组，共有多少种分法？

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。

5人队伍中男多于女，男生人数只能为3、4、5。分别计算选法，再除以所有等可能的5人选法。

The team must contain either 3, 4 or 5 men. The corresponding numbers of selections are

There are $\binom{15}{5}=3003$ equally likely teams. Hence

也可以想象按次序不放回抽5人。先算每一种男女次序的概率，再乘相应的次序数。

Imagine selecting the five members in order, without replacement. The probabilities of 5 men, 4 men and 3 men are respectively

The factors $\binom54$ and $\binom53$ account for the possible positions of the men. Therefore,

各组人数不同，按人数即可区分三个组，不需要再除以组的排列数。

Choose the group of 6, then the group of 4 from the remaining 7 members. The final 3 members form the last group. Thus the number of divisions is

No division by $3!$ is needed because the three groups have different sizes.

把13人排成一列，前6、中间4、最后3人分组。每组内部的排列不改变分组，因此除以三个内部排列数。

Arrange all 13 members in a row and divide the row into consecutive groups of 6, 4 and 3.

Permuting the members within a group does not change the division, so the required number is