princetonreview 一道数学题

nolanchen

Two couples and one single person are seated at random in a five chairs. What is the probability that neither of the couples sits together in adjacent chairs?

A. 1/5

B: 1/4

C: 3/8

D: 2/5

E: 1/2

Answer: D

这题怎么解呀?

jandjshi

怎么我算来算去是3/5呢? NN来看看.

moomoo

A-B C-D E

all possible arrangements : P(5, 5)

arrangements with A-B ajacent: P(4, 4) * P(2,2) - consider AB as one entity, which can be in the order AB or BA

arrangements with C-D ajacent: P(4, 4) * P(2,2)

arrangements with A-B, and C-D ajacent: P(3,3) * P(2,2) * P(2,2)

1 - (P(4,4)*P(2,2) + P(4,4)*P(2,2) - P(3,3)*P(2,2)*P(2,2))/P(5,5) = 2/5

[此贴子已经被作者于2006-8-3 13:12:52编辑过]

jandjshi

why P(5,5) when there are only 3 ppl?

jandjshi

以下是引用jandjshi在2006-8-3 13:21:00的发言：
why P(5,5) when there are only 3 ppl?

sorry, didn't see 2 couples. 打PP. I got it, thanks.

顺便看下a couple and a stranger是不是3/5.

[此贴子已经被作者于2006-8-3 13:45:42编辑过]

mymengming

以下是引用moomoo在2006-8-3 13:11:00的发言：

A-B C-D E

all possible arrangements : P(5, 5)

arrangements with A-B ajacent: P(4, 4) * P(2,2) - consider AB as one entity, which can be in the order AB or BA

arrangements with C-D ajacent: P(4, 4) * P(2,2)

arrangements with A-B, and C-D ajacent: P(3,3) * P(2,2) * P(2,2)

1 - (P(4,4)*P(2,2) + P(4,4)*P(2,2) - P(3,3)*P(2,2)*P(2,2))/P(5,5) = 2/5

同意,很牛的说