Online Course Discussion Forum

AMC 10

Picture of Kai Ho Liang
AMC 10
by Kai Ho Liang - Sunday, December 13, 2020, 9:17 PM

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

Picture of Leo Zeng
Re: AMC 10
by Leo Zeng - Monday, December 14, 2020, 9:06 AM


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.