Prove that value of zero factorial is 1.

Solution :

We have, P(n, r) = \(n!\over (n – r)!\)

Putting r = n,

\(\implies\)  P(n, n) = \(n!\over 0!\)

\(\implies\)  n! = \(n!\over 0!\)               [ \(\because\)  P(n, n) = n! ]

\(\implies\)  0! = \(n!\over n!\)  = 1

Hence, Proved.