题目
(a) Find the number of different arrangements of the 8 letters in the word COCOONED.
(b) Find the number of different arrangements of the 8 letters in the word COCOONED in which the first letter is O and the last letter is N.
(c) Find the probability that a randomly chosen arrangement of the 8 letters in the word COCOONED has all three Os together given that the two Cs are next to each other.
题目中文翻译
(a) 求单词 COCOONED 的 8 个字母的不同排列个数。
(b) 将单词 COCOONED 的 8 个字母排列，要求第一个字母为 O，最后一个字母为 N，求不同排列的个数。
(c) 随机选取单词 COCOONED 的 8 个字母的一种排列，已知两个 C 相邻，求三个 O 全部相邻的概率。
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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两C与三O分别重复，其余字母不同。
答题过程
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(b)
解法一
思路
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固定首O末N，内部剩两C两O与E、D。
答题过程
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After fixing O first and N last, the six remaining letters contain two Cs and two Os. Thus
(c)
解法一
思路
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条件是CC相邻，分母仅数CC作块的排列；分子同时把CC与OOO都作块。
答题过程
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Given that the Cs are together, treat CC as one object. With O, O, O, N, E, D, there are arrangements.
If the Os are also together, the five distinct objects CC, OOO, N, E, D have arrangements. Hence