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 S and all si's
are distinct}, and
Y
=
{(s1, s2, ,
sk) | si S and s1 <
s2 < < sk}.
(a) Define a one-to-one correspondence
f : X → Y.
Explain...