Answer :

(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


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