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Prove that (n!)! is divisible by (n!)^(n-1)!

  1. Jan 12, 2012 #1
    Prove that (n!)! is divisible by (n!)^(n-1)!
     
  2. jcsd
  3. Jan 12, 2012 #2

    jedishrfu

    Staff: Mentor

    Re: Divisible

    first try playing with n=2 then n=3 then n=4 and see if you can find a pattern and only evaluate the n! itself not everything to see the pattern

    (2!)! = 2! and (3!)! = 6! and (4!)!=24! vs (2!)^(1!)= 2^1 ...

    Next I think you need to use induction to prove it.
     
  4. Jan 12, 2012 #3

    micromass

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    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    Re: Divisible

    Are you familiar with multinomial coefficients??
     
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