# Prove that ""^(n+1)P_r=((n+1))/((n-r+1))xx""^nP_r?

Sep 14, 2016

#### Answer:

Please see below.

#### Explanation:

The formula for the number of possible permutations of $r$ objects from a set of $n$ is written as ""^nP_r and is

""^nP_r=(n!)/((n-r)!),

where k! is defined as k! =kxx(k-1)xx(k-2)...3xx2xx1

Hence ""^(n+1)P_r=((n+1)!)/((n+1-r)!)=((n+1)!)/((n-r+1)!)

= ((n+1)xxn!)/((n-r+1)xx(n-r)!)

= ((n+1))/((n-r+1))xx(n!)/((n-r)!)

= ((n+1))/((n-r+1))xx""^nP_r