Prove that

(i) = n(n – 1) (n – 2) …. (r + 1)

(ii) (n – r + 1).

(iii)

(i) To Prove :

Formula :

Writing (n!) in terms of (r!) by using above formula,

=

Cancelling (r!),

= n(n - 1)(n - 2)…. (r + 1)

= R.H.S.

∴LHS = RHS

Note : In permutation and combination r is always less than n, so we can write n! in terms of r! by using given formula.

(ii) To Prove :

Formula :

by using above formula,

Cancelling (n - r + 1),

= R.H.S.

∴LHS = RHS

(iii) To Prove :

Formula :

by using above formula,

Taking common,

= R.H.S.

∴LHS = RHS