Question

How do you simplify `n(n-1)!`?

Answer 1

`n(n-1)! =n!`

Explanation:

A number represented by `a!` (where `a` is a natural number) is

`axx(a-1)xx(a-2)xx....xx4xx3xx2xx1`

i.e. product of all the numbers from `a` downwards till `1`,

Hence, `(n-1)! =(n-1)xx(n-2)xx(n-3)xx....xx4xx3xx2xx1`

and `n(n-1)!` is

`nxx[(n-1)xx(n-2)xx(n-3)xx....xx4xx3xx2xx1]`

or `nxx(n-1)xx(n-2)xx(n-3)xx....xx4xx3xx2xx1`

But this is `n!`

Hence `n(n-1)! =n!`