(a) 将单词 INTELLECT 中的 9 个字母排列，要求两个 T 相邻。共有多少种不同的排列？

(b) 将单词 INTELLECT 中的 9 个字母排列，要求两端各有一个 T，且两个 E 不相邻。共有多少种不同的排列？

从单词 INTELLECT 中的 9 个字母中随机选取 4 个字母。

(c) 求包含至少一个 E 和恰好一个 T 的选取结果占所有可能选取结果的百分比。

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。

两T作为一个块，共8个对象，其中E和L分别重复两次。

Treat TT as one object. The eight objects contain two identical Es and two identical Ls, so

两端固定T，先排其余7个字母，再减去两E相邻的排列。

With a T fixed at each end, the seven interior letters are I, N, E, E, L, L and C. There are $\frac{7!}{2!\,2!}$ arrangements in total.

If the Es are together, treat EE as a block. There are then six objects with two identical Ls, giving $\frac{6!}{2!}$ arrangements. Thus

也可以先排I、N、L、L、C，再在六个不同空隙中放两E。

Fix the Ts at the ends. Arrange I, N, L, L and C in $\frac{5!}{2!}$ ways inside them. These five letters create six gaps, including the gaps next to the Ts.

Place the two identical Es in two distinct gaps. Hence

随机选的是9个实际字母牌，等概率样本数为9选4。按选到一个E或两个E分类，均须恰一个T。

There are $\binom94=126$ equally likely selections of four individual letters.

Of the nine letters, two are E, two are T and five are neither E nor T. The permitted selections have compositions TE plus two other letters, or TEE plus one other letter. Their number is

The required percentage is

也可以先数恰一个T的选法，再减去没有E的情况。

There are $\binom21\binom73=70$ selections containing exactly one T.

Of these, $\binom21\binom53=20$ contain no E. Thus the required percentage is