Answer to Question #252564 in Discrete Mathematics for suu

Question

Prove that

(

)

(

)

1,

1

,

nPnnPnn

 − − =

.

Answer 1

Prove that $^nP_{n}=^nP_{n-1}$

Proof:

$^nP_{n}=n!$

$^nP_{n-1}=\frac{n!}{[n-(n-1)]!}=\frac{n!}{1}=n!$