题目
(a) Find the number of different arrangements of the 8 letters in the word DECEIVED in which all three Es are together and the two Ds are together.
(b) Find the number of different arrangements of the 8 letters in the word DECEIVED in which the three Es are not all together.
题目中文翻译
(a) 求单词 DECEIVED 中 8 个字母的不同排列数，要求三个 E 全部相邻，且两个 D 相邻。
(b) 求单词 DECEIVED 中 8 个字母的不同排列数，要求三个 E 不全部相邻。
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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EEE与DD各作一个块，与C、I、V构成五个不同对象。
答题过程
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The five distinct objects EEE, DD, C, I and V have
arrangements.
(b)
解法一
思路
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先数全部重复字母排列，再减去EEE全相邻的情况；不是要求所有E两两不相邻。
答题过程
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The total number of arrangements is .
If all Es are together, the EEE block and D, D, C, I, V have arrangements. Thus