If `""^(n)P_(4)=1680,` find n.

Explanation

Given `""^(n)P_(4)=1680`
But `""^(n)P_(4)=n(n-1)(n-2)(n-3).`
Thus, we are given `n(n-1)(n-2)(n-3)`
`=1680 =8xx7xx6xx5`
On comparing the largest integers on bothsides, we get n=8.