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Question: 13 this exercise outlines a bijective proof of the formula...

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13. This exercise outlines a bijective proof of the formula (2) 1 from Section 1.1. Let A be the set of k-multisets taken from [n] and let B be the set of k-subsets of [k +n- . ak) is written in nondecreasing order: a1S a2 < ak. Define f : A--B by Assume that the k-multiset a.a2. This function, and proof, is originally due to Euler (a) Prove that the outputs of f are indeed k-subsets of [k + n 1. This requires proof since it is not immediately clear from the definition of f (b) Prove that f is a bijection.

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