Prep 一题想不明白

elisalu7 · 发表于 2012-9-17 15:49:08

Q: A certain law firm consists of 4 senior partners and 6 junior partners. How many different group of 3 partners can be formed in which at least one member of the group is a senior partner? (Two groups are considered different if at least one group member is different. )
A: 100

解答是C(10,3)-C(6,3) 用的是排除法
但是我如果考虑三个人，为什么不可以4*9*8/3!=48 就不对呢？这里有什么地方考虑错了呢？

sonicwolf · 发表于 2012-9-17 16:34:41

一个senior C(4,1)*C(6,2)
二个senior C(4,2)*C(6,1)
三个senior C(4,3)

60+36+4=100

error703 · 发表于 2012-9-17 16:59:49

Q: A certain law firm consists of 4 senior partners and 6 junior partners. How many different group of 3 partners can be formed in which at least one member of the group is a senior partner? (Two groups are considered different if at least one group member is different. )
A: 100

解答是C(10,3)-C(6,3) 用的是排除法
但是我如果考虑三个人，为什么不可以4*9*8/3!=48 就不对呢？这里有什么地方考虑错了呢？

-- by 会员 elisalu7 (2012/9/17 15:49:08)

3！的用法不是这样用的吧。应该是10个人里任意选3个，那么算组合的话要除以3!

limo8921 · 发表于 2012-9-17 18:11:02

需要反着想比较快吧。
至少有一个senior partner的反义是一个senior也没有。用全部情况再减去一个senior也没有的情况，就是答案。
全部情况是：C（3,10）
一个senior也没有的情况是：C（3,6）
最后一减。

LZ的思路没明白哦

elisalu7 · 发表于 2012-9-17 20:08:57

恩，明白了，谢谢大家！

Prep 一题想不明白

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