Prove that, for all real numbers r and all integers k and m,
C(r,m)C(m,k)=C(r,k)C(r-k,m-k)
Where C(r,m) is r choose m.
I'm terrible at these proofs because I never know which identity is needed to start.
Any help?
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)