How many committees are possible?
I added the total number of women ($17$) and the total number of men ($21$) to get $38$ total people.
I used this as my $n$ or objects. I then subtracted my $r$ from $n$ and got $31$.
So $\frac{n!}{(n-r)!} = \frac{38!}{31!}= 63,606,090,245$
This number seems too large, but perhaps it's not? Did I calculate this properly?
Note that this would be combination since the order is not taken into account. $$\displaystyle \binom{38}{7} = \dfrac{38!}{7!31!} = \dfrac{32\cdot 33\cdot 34\cdot 35\cdot 36\cdot 37\cdot 38}{1\cdot 2\cdot 3\cdot 4\cdot 5\cdot 6\cdot 7}$$