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