1. 10 different Chinese magazines and 4 different English magazines are arranged in a row.If any 2 English magazines cannot be placed nect to each other, explain why there are 28740096000 permutations.
2. 6 different Chinese books and 8 different English books are arranged in a row. If only 4 Chinese books are placed next to each other, explain why there are 304819200 different permutations.
請給詳細解釋,謝謝,同埋條題目就係咁樣- -無其他野要補充
PROB問題78912748291749
2012-12-10 12:24 am
回答 (2)
2012-12-10 5:33 am
✔ 最佳答案
1.Step 1 : Arrange the 10 Chinese magazines (C) in a row as below (10P10).
_C_C_C_C_C_C_C_C_C_C_
Step 2 : Put the 4 English magazines in any 4 "_" out of the 11"_" (11P4).
Number of different permutations
= 10P10 x 11P4
= (10!) x (11!/7!)
= 3628800 x 7920
= 28740096000
======
2.
Step 1: Arrange the 8 different English books (E) in a row as below (8P8):
_E_E_E_E_E_E_E_E_
Step 2: From the 6 Chinese books, choose 4 Chinese books and their arrangementis not considered (6C4).
Step 3 : Put the set in the above step and the rest 2 Chinese books in any 3"_" out of the 9 "_". (9P3).
Number of different permutations
= 8P8 x 6C4 x 9P3
= (8!) x (6!/2!4!) x (9!/6!)
= 40320 x 15 x 504
= 304819200
In my opinion, the internal permutation of the set of 4 books should beconsidered.
Therefore, the number of different permutations
= 304819200 x 4P4
= 304819200 x 4!
= 7315660800
參考: andrew
2012-12-10 4:05 am
Can you check check Q2?
收錄日期: 2021-04-13 19:10:11
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20121209000051KK00188