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

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Answer 1 · 2016-10-25T14:32:30

$n (n - 1)! = n!$ $n(n-1)! =n!$

A number represented by $a!$ $a!$ (where $a$ $a$ 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 $n(n-1)! =n!$

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