Author Topic: Day care center seating arrangements  (Read 2470 times)

PuraVidaQQSH

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Day care center seating arrangements
« on: 十二月 10, 2013, 10:45:48 pm »
A day care center takes 7 boys and 3 girls
to an afternoon movie. The children sit together
in one row of 10 seats, but none of the girls are
sitted next to each other. How many different
seating arrangements are possible?

warren

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Re: Day care center seating arrangements
« Reply #1 on: 七月 07, 2014, 02:09:53 pm »
好久没来了,这里好冷清啊

可能的排列数是多项式 (x+x^2+x^3+...)(x^2+x^3+x^4+...)(x^2+x^3+x^4+...) (1+x+x^2+x^3+...)
的10次项系数, 即 (1+x+x^2+x^3+...)^4=(1-x)^(-4) 的5次项系数,56.


万精油

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Re: Day care center seating arrangements
« Reply #2 on: 七月 16, 2014, 01:19:46 pm »
冷清的原因是因为你们这些高手都跑了。大家都来,这里就热闹了。

另外,你这个解没有考虑到Boys或Girls之间互相换位的情况。从字面上看,应该有这个要求。

warren

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Re: Day care center seating arrangements
« Reply #3 on: 七月 18, 2014, 02:32:08 am »
以前一些活跃会员现在来得少了,不热闹了.

是的,应当考虑到Boys或Girls之间互相换位的情况, 排列数应是56*3!*7!.