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【题目】这六个数字.

(1)能组成多少个无重复数字的四位偶数?

(2)能组成多少个无重复数字且为的倍数的五位数?

(3)能组成多少个无重复数字且比大的四位数?

【答案】(1)(2)(3)

【解析】(1)符合要求的四位可分为三类:第一类:在个位时有个;

第二类:在个位时,首位从中选定个(有种),十位和百位从余下的数字中选(有种),于是有个;

第三类:在个位时,与第二类同理,也有由分类加法计算原理知,共有四位偶数个.

(2)符合要求的五位数可分为两类:个位数上的数字是的五位数有个,个位数上的数字是的五位数有个,故满足条件的五位数的个数共有个.

(3)比大的四位偶数可分为三类:

第一类:形如共有个;

第二类:形如, 共有个;

第三类:形如,共有个.

由分类加法计数原理知,无重复数字且比大的四位数共有个.

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