Question

11. Explain why nPn=n! for all positive integers n.

Answer 1

`^nP_r=n!` Proved.

Explanation:

Consider the provided information.

We need to explain why
`^nP_n=n!` for all positive integers n.

The permutation formula is:
`^nP_r=(n!)/((n-r)!)`

Now substitute r=n in above formula as we want the value of
`^nP_n`

`^nP_n=(n!)/((n-n)!)`

`^nP_r=(n!)/((0)!)`

The value of 0! is 1.

Therefore,

`^nP_r=(n!)/(1)`

`^nP_r=n!`

Hence, proved.