Question 7: Let a > 0, b > 0, and n > 0 be integers, and consider the set S = How many subsets of size a +b+1 does S have? Let k be an integer with 0 Sk n. Consider subsets T of S such that ITab+1 and the (a1)-st smallest element in T is equal to a+ k+1. How many such subsets T are there? . Use the above results to prove that a +b+n1 2-k