Summation of Products of Binomial Coefficients

[Vespero]

Homework Statement

Find and prove a formula for sum{ (m1 choose r)(m2 choose s)(m3 choose t) }

where the sum is over all nonnegative integers r, s, ant t with fixed sum r + s + t = n.

Homework Equations

The Attempt at a Solution

I first attempted to find the number of combinations of r, s, and t would satisfy r + s + t = n.
I found this to be (n+1)(n+2)/2. I have a feeling this is important (it gives the number of terms in the summation), but can't seem to find a way to apply it to find a formula.

 

[ystael]

Rather than trying to evaluate this sum using algebra, try to find a combinatorial model for it -- a scenario where the sum you have is obviously the number of different ways to do something. Then count that model in a simpler way.