First slide

Binomial theorem for positive integral Index

Question

If $m$ and $n$ are positive integers, then value of $^{m} {C_{0}}^{n} C_{k} +^{m} {C_{1}}^{n} C_{k - 1} + \dots +^{m} {C_{k}}^{n} C_{0}$

Moderate

A

$^{m + n} C_{k}$
B

$^{m + n} C_{m + k}$
C

$^{m + n} C_{n + k}$
D

none of these

Solution

Given expression
= number of ways of choosing persons out $m$ men
and $n$ women $^{m + n} C_{k}$

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