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

1 Answer
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#