A person wishes to make up as many different parties as he can out of 20 friends ,each party consisting of the same number .how many shhould he invite at a time?(tis es clear ..10)In how many of these would the same man be found?

I think the answer is 19c₉ parties for which for a man will be found.If correct,I will explain.

It is clear that 10 people shud be called at a time for max. no of parties.Now,let us consider a group of ten friends which consista of a friend A.Now,keep A aside and select other friends (9+10remaining) to make diff. groups.This can be done in 19c₉ ways.In all these groups,a particular friend A will be there.So,the ans is 19c₉ ways.