Choosing $2$ groups of $5$ members and $1$ group of $2$ members from $15$ person 
In how many ways can we choose $2$ groups of $5$ members and $1$ group of $2$ members from $15$ person?
Additional info: groups are not labeled.

Things I have done so far: I know number of ways to choose $3$ groups of $5$ members from $15$ person is equal to $$\frac{{15 \choose 5}{10 \choose 5}}{3!}$$
However i'm not sure which is true about this question$$\frac{{15 \choose 5}{10 \choose 5}{5 \choose 2}}{3!}$$
or
$$\frac{{15 \choose 5}{10 \choose 5}{5 \choose 2}}{2!}$$

So the answer is: $\frac{{15 \choose 5} {10 \choose 5} {5 \choose 2} {3 \choose 3}}{2!}$
The reason for 2! in the denominator is, that here are 2 groups, which have the same number of group members (5).
For example: $1,2,3,4,5 - 6,7,8,9,10$ is the same like $6,7,8,9,10-1,2,3,4,5$
