Easier to think of this through combinatorics.
Left hand side:
r = number of people
m= # of people being chosen for some committee from the group of r people.
k = Choosing k people out of the committee of m people for some special role (say senators).
Right hand side
Choosing k people who will be senators and in a committee. Then you designate the remaining empty committee spots (m-k) to the left over people (r-k)