the question is: 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?