If `r lt s le n " then prove that " ^(n)P_(s) " is divisible by "^(n)P_(r).`

Explanation

We have
` ""^(n)P_(s)=n(n-1)(n-2) ...(n-r+1)(n-r)...(n-s+1)`
`={n(n-1)(n-2)...(n-r+1)}xx{(n-r)(n-r-1) ...(n-s+1)}`
`= ""^(n)P_(r)xx{(n-r)(n-r-1)...(n-s+1)},` which is clearly divisible by ` ""^(n)P_(r).`
Hence, ` ""^(n)P_(s)` is divisible by ` ""^(n)P_(r).`