Is it possible to prove the following identity using combinatorial argument :
[n∑k=0(nk)]2=2n∑k=0(2nk)
Answer
Suppose that you have a group of n mixed couples. The lefthand side is the number of ways to choose a set of k men and a set of ℓ women for some k,ℓ∈{0,…,n}; the righthand side is the number of ways to choose an arbitrary subset of the group. Clearly these are the same.
No comments:
Post a Comment