The question is:

36 people are to be divided into groups of 6. Four of the boys insist on being in the same group as each other and 3 of the girls also want to be in the same group as each other. How many ways can the 36 people be divided into the groups?

This is how I went about answering it:

4 boys are put into one group. Two more individuals are required to make up a group of 6. 3 girls are put into another group. 3 more individuals are required to make up this group.

We have 29choose2 multiplied by 27choose3 to make up these two groups.

Then ofcourse the remaining 24 can be allocated to 4 indistinguishable groups by (24+6-1)choose6 i.e. 29choose6.

My final answer is 406+2925+475020 = 478,351

Just wanted some feedback as to whether I'm doing it right? Thanks.