【題目】這六個(gè)數(shù)字.

(1)能組成多少個(gè)無重復(fù)數(shù)字的四位偶數(shù)?

(2)能組成多少個(gè)無重復(fù)數(shù)字且為的倍數(shù)的五位數(shù)?

(3)能組成多少個(gè)無重復(fù)數(shù)字且比大的四位數(shù)?

【答案】(1)(2)(3)

【解析】(1)符合要求的四位可分為三類:第一類:在個(gè)位時(shí)有個(gè);

第二類:在個(gè)位時(shí),首位從中選定個(gè)(有種),十位和百位從余下的數(shù)字中選(有種),于是有個(gè);

第三類:在個(gè)位時(shí),與第二類同理,也有個(gè),由分類加法計(jì)算原理知,共有四位偶數(shù)個(gè).

(2)符合要求的五位數(shù)可分為兩類:個(gè)位數(shù)上的數(shù)字是的五位數(shù)有個(gè),個(gè)位數(shù)上的數(shù)字是的五位數(shù)有個(gè),故滿足條件的五位數(shù)的個(gè)數(shù)共有個(gè).

(3)比大的四位偶數(shù)可分為三類:

第一類:形如共有個(gè);

第二類:形如, 共有個(gè);

第三類:形如,共有個(gè).

由分類加法計(jì)數(shù)原理知,無重復(fù)數(shù)字且比大的四位數(shù)共有個(gè).

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