Given 30 people,in how many possible ways there are 6 months having birthday of 2 people each and 6 months having birthday of 3 people each. 

My attempt: 

There are ${12 \choose 6}$ ways of selecting the 6 months having 2 birthdays each, and we automatically select the other six months having 3 birthdays each.

Now, we can classify the months as 12 boxes, and the people as balls. So, we can arrange and permute the people in $30!$ ways. 

I don't think we need to find the arrangements of the month and I don't think that I have the correct answer yet, I think I am overcounting and I don't know where. Please help. Thank you.