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Let S be a set of n numbers. Let X be the set of all subsets...

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Advance Math

Let S be a set of n numbers. Let X bethe set of all subsets of S of size k, and letY 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'sare distinct}, and
Y={(s1, s2,   ,sk) | si  S and s1 2 <    < 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|=

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