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AMC 10

 
 
LiangKai Ho的头像
AMC 10
LiangKai Ho - 2020年12月13日 Sunday 21:17
 

Can someone help explain the below problem in details? thank you!

Adam, Benin, Chiang, Deshawn, Esther, and Fiona have internet accounts. Some, but not all, of them are internet friends with each other, and none of them has an internet friend outside this group. Each of them has the same number of internet friends. In how many different ways can this happen?

(A) 60(B) 170(C) 290(D) 320(E) 660



 
ZengLeo的头像
Re: AMC 10
ZengLeo - 2020年12月14日 Monday 09:06
 

Hi,

What I've found out is that the most number of friends one person can have is 4, since they have the same number of friends. Also, the cases for 1 and 4 are the same, since for 4, you can take the cases for 1 and turn them into not-friends. Same for 2 and 3. So you have to first find out the cases for 1 and 2, then multiply by two.

 
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