Probability theory - Combinatorics

to avoid inmates becoming close friends, they are put into groups where they end up with other inmates.

In how many ways can the prison warden divide 6 inmates into

a) two equally large groups? b) two groups (equally or different group sizes)?

I understand that the inmates can be divided into say: group A and group B and that 3 specific inmates in group A is equivalent to putting the same 3 in group B, thus ''double-counting''.

There should be an easy way to apply this to a formula but I can't seem to get it right, any suggestions??

the answers are:

a) 10 b) 31

thanks on beforehand