I've been wondering for a while how to solve (prove) a combinatorial identity, using just combinatorial interpretation:
m∑i=02n−i(ni)(mi)=n∑i=0(n+m−im)(ni)
(m≤n )
The left hand side is pretty much about choosing any number of elements from the set M={a1,…,am} and then choosing at least the same amount from N={b1,…,bn}, but I can't see how the right hand side satisfies that.
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