If x,y and r are positive integers, then ^x{Cᵣ}{ + ^x}{C_{r - 1}}^y{C₁}{ + ^x}{C_{r - 2}}^y{C₂

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Gujarati

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6.Permutation and Combination

easy

If $x,\;y$ and $r$ are positive integers, then $^x{C_r}{ + ^x}{C_{r - 1}}^y{C_1}{ + ^x}{C_{r - 2}}^y{C_2} + .......{ + ^y}{C_r} = $

A

$\frac{{x\;!\;y\;!}}{{r\;!}}$

B

$\frac{{(x + y)\;!}}{{r\;!}}$

C

$^{x + y}{C_r}$

D

$^{xy}{C_r}$

Solution

(c) The result is trivially true for $r = 1,\;2$.

It can be easily proved by the principle of mathematical induction that the result is true for $r$ also.

Standard 11

Mathematics

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