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

sothea hoeung · Jan 12, 2012

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

jedishrfu · Jan 12, 2012

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.

micromass · Jan 12, 2012

Are you familiar with multinomial coefficients??

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

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