Find `n"if" P (n,4)=12.P(n,2)`

Explanation

`""^nP_4=12xx""^nP_2`
` or,(n!)/((n-4)!)=12xx(n!)/((n-2)!)`
`or, (n-2)! =12(n-4)!`
`or,(n-2)(n-3)(n-4)! =12(n-4)!`
`or,(n-2)(n-3)=12`
`or,n^2-5n-6=60`
`(n-6)(n+1)=0`
`or, n=6-1`
Hence `n=6` as n is a natural number.