Question: Assume that 0 m n. Give a combinatorial proof that ( m n ) = k = m n ( m 1 k 1 )

Assume that 0 m n. Give a combinatorial proof that(mn)=k=mn(m1k1)

Hint: how many m-element subsets of {1, 2, . . . , n} are there which have k as the largest element? Plug in m = 2 here, what familiar formula do you get?

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