Hi,

I have been asked to derive a simple closed form expression for the
following sum:

n
∑ (-1)^(m+i) *(nCi)*(iCm) = S n, m
i = m

[with m = 0,1,2,....,n ; n= 0,1,2,....] and C is the combinations symbol.


I know that we are meant to be using the binomial theorem but I dont quite know where to go from there. Any help would be much appreciated.