The correct option is D ^nC_r + 2^nC_r 1 + ^nC_r 2 = ^nC_r + ^nC_r 1 +^nC_r 1 + ^nC_r 2 = ^n+1C_r + ^n+1C_r 1 = ^n+2C_r ...

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Binomial Coefficients

n Cr+2n Cr-1+...

Question

$^{n} C_{r} + 2^{n} C_{r - 1} +^{n} C_{r - 2}$ =

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Solution

The correct option is C

$^{n} C_{r} + 2^{n} C_{r - 1} +^{n} C_{r - 2}$ = $^{n} C_{r} +^{n} C_{r - 1} +^{n} C_{r - 1} +^{n} C_{r - 2}$

= $^{n + 1} C_{r} +^{n + 1} C_{r - 1}$ = $^{n + 2} C_{r}$

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Similar questions

Evaluate $^{n} C_{r} + 2^{n} C_{r - 1} +^{n} C r - 2 .$

^{n} C_{r + 1} + 2^{n} C_{r} +^{n} C_{r - 1} =

^{n} C_{r} + 2^{n} C_{r - 1} +^{n} C_{r - 2}

^{n} C_{r + 1} + 2^{n} C_{r} +^{n} C_{r - 1} =

2 \leq r \leq n,

^{n} C_{r} + 2^{n} C_{r - 1} +^{n} C_{r - 2}

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