Factorial of Factorial

Find the number of non-negative integers n n satisfying the following equality─

( n ! ) ! = n ! \large \color{#3D99F6}(n!)! = n!


The answer is 3.

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1 solution

Charlie Feinson
Dec 29, 2017

True when n=n!. This is true for only 3 non-negative integers.

(0!)! = 0 = 0!

(1!)! = 1 = 1!

(2!)! = 2 = 2!

The 3 numbers are right, but your solution for 0 is wrong. 0! is 1, not 0. See this link: https://zero-factorial.com/whatis.html

One reason that 0! is 1 is because factorial is the number of ways to arrange something.

The number of ways to arrange 0 things is 1: to do nothing!

Siva Budaraju - 3 years, 5 months ago

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More formally, Factorials is a way of representing permutations

Mohammad Farhat - 2 years, 9 months ago

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