烦请大家看一道排列组合题，谢谢！

lianghao

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

A. 48

B. 100

C. 120

D. 288

E. 600

答案是B，我对排列组合做得不太好，怎么也没推出来。不知可否有人解答一下疑惑呢？万分感谢！

sjjay

分三种情况，只有一个senior ，有2个senior，3个都是senior

所以答案应该是c4(1)*c(6)2+c4(2)*c6(1)+c4(3)=60+36+4=100

myinterzj

考虑10个人是个整体，从中选取3个，即C10（3），减去全部都是junior partner的组合数C6（3），剩下的组合肯定都包含至少一个senior partner

所以结果就是C10（3）-C6（3）=100

zhongtiangg

支持楼上