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Homework Help: Induction? question

  1. Feb 20, 2008 #1
    [SOLVED] induction? question

    1. The problem statement, all variables and given/known data

    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?

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Feb 20, 2008 #2


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    Science Advisor
    Homework Helper

    Why do you need induction if you have a proof without it?
  4. Feb 20, 2008 #3
    because the professor said something about induction. he said to "select from a pool" (of k's i guess, whatever that means) and then use induction over n. he said to check for n=1 and n=2 and show that the statement holds for n>= 2. he does seem kind of out of it though. to use induction how would i proceed? i need to combine some expression with
    k!/(k1! · · · kn!)

    right? i can't find this expression. the only sort of induction i can get is a logically inherent one using the choose function.
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