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

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

Answers and Replies

  • #2
12,235
5,941


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.
 
  • #3
22,089
3,291


Are you familiar with multinomial coefficients??
 

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