In how many different ways can 5 identical blue books, 3 identical yellow books, 1 black book and 1 pink book be distributed amo

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问题 In how many different ways can 5 identical blue books, 3 identical yellow books, 1 black book and 1 pink book be distributed among 10 students such that each student receives a book?

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答案5040

解析本题目中5本蓝色的书完全相同，3本黄色的书也完全相同，剩下2本书不同。解决这种问题可以采用以下的步骤：
(1)先用组合数分配相同元素。从10人中选出5人拿蓝色的书，有C₁₀⁵种可能；再从剩下的5人中选出3人拿蓝色的书，有C₅⁵种可能。
(2)再用排列数分配不同元素。还剩下2人和2本不同的书，有A₂²种分配方式。
(3)将以上步骤之间用乘法连接，即一共有C₁₀⁵C₅⁵A₂²=5040种可能。

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