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let k, n, and k1, . . . , kn be given natural numbers, such that

k1 + . . . + kn = k.

Assume that k musicians shall be distributed to n orchestras such that exactly

ki musicians play in the ith orchestra. Prove that there exist exactly

k!/(k1! · · · kn!)

different distributions.

is it possible to use induction to answer this? i can prove it by using the choose function to find all the possible distributions. in that way i get a proof for the statement, but i am unable to assume that it is correct for n, and then show it is correct for n+1. can someone give me some ideas?

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# Induction? question

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