Let S be a set of n numbers. Let X be the set of all subsets of S of size k, and let Y be the set of all ordered k-tuples (s1, s2, , sk) such that s1 < s2 < < sk. That is, X = {{s1, s2, , sk} | si is in S and all si's are distinct}, and Y = {(s1, s2, , sk) | si is in S and s1 < s2 < < sk}. (a) Define a one-to-one correspondence f : X → Y. Explain why f is one-to-one and onto. (b) Determine |X| and |Y|.

|X| =

|Y| =

Can someone please answer part b of this question. The answer available is incorrect and unclear.