please help ! Form 6 maths (Permutation & Combinations)

用戶113807

2008-02-13 10:39 pm

Four couples reserved eight seats in a row at a concert. How many different sitting arrangements are possible if:
a) Anyone can be seated anywhere
b) Each couple has to be seated together
c) All the ladies want to seat together

回答 (2)

[匿名]

2008-02-13 11:56 pm

✔ 最佳答案

Q: Four couples reserved eight seats in a row at a concert.
How many different sitting arrangements are possible if:
( a ) Anyone can be seated anywhere
( b ) Each couple has to be seated together
( c ) All the ladies want to seat together
Sol:
( a )
8! ＝ 40320
( b )
把每對夫妻都視同 1 人, 共 4 對
方法有 4!
每對夫妻排列方式有 2 種, 4 對共 24
所以排列方式共有
4! * 24
＝ 24 * 16
＝ 384
( c )
把 4 位女士視同 1 人, 連同 4 位男士共 5 人
排列方式有 5!
4 位女士之間的排列方式有 4!
所以排列方式共有
5! * 4!
＝ 120 * 24
＝ 2880
Ans: ( a ) 40320 ( b ) 384 ( c ) 2880

參考: 數學小頭腦

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[匿名]

2008-02-18 8:08 pm

( a ) 40320 ( b ) 384 ( c ) 2880

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