permutation & Combination

2013-01-13 5:56 am

There are 12 different books on a desk,where 5 of them are Chinese books,
4 of them are English books and the remaining are French Books.
The books are arranged in a row.

a.If any 2 English books cannot be placed next to each other,
find the no of permutation.

b.If only 3 Chinese books are placed next to each other,
find the no of permutation.

c.If the books placed at the two ends must be Chinese books,
find the no of permutation.

d.If If English books cannot be placed at two ends,
find the no of permutation.

e.If Chinese books cannot be placed at both ends at the same time,
find the no of permutation.

更新1:

唔係好明 b )place 3 boxes(1 big 2 small) among 8 cracks, there are 8P3 / 2! method 8P3 / 2! 點解？

回答 (1)

50418129

2013-01-14 7:52 pm

✔ 最佳答案

Denote E for English, C for Chinese, F for French.

(a)

place 5C and 3F, there are 8P8 methods
place 4E among 9 cracks, there are 9P4 methods
so, required no. = 8P8 x 9P4

(b)

place 4E and 3F, there are 7P7 methods
place 3 boxes(1 big 2 small) among 8 cracks, there are 8P3 / 2! method
place 5C into boxes, there are 5P5 method
so, required no. = 7P7 x 8P3 x 5P5 / 2!

(c)

place 2C at the two ends, there are 5P2 methods
place the other 9 books, there are 9P9 methods
so, required no. = 5P2 x 9P9

(d)

place 2(not E) at the two ends, there are 8P2 methods
place the other 9 books, there are 9P9 methods
so, required no. = 8P2 x 9P9

(e)

place 2F at the two ends, there are 4P2 methods
place the other 9 books, there are 9P9 methods
so, required no. = 4P2 x 9P9

2013-01-16 10:23:40 補充：
因為兩個細既盒視為且一樣的東西，佢地交換係一樣，所以每個情況重覆 2! 次，所以咪要除返 2! 囉

參考: knowledge

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