Suppose you have a group of 10 people a How many ways are th

Suppose you have a group of 10 people.

(a) How many ways are there to separate these 10 people into two groups, if no group can have less than 2 people? [Hint: when dividing into two groups, you only have to figure out who is in one group, since then the other one is determined.]

(b) How many ways are there to separate these 10 people into two groups of 5 each? [Hint: there is a subtle issue of overcounting here and in (c).]