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

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Solution

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

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

= $^{n + 1} C_{r} +^{n + 1} C_{r - 1} [∵^{n} C_{r} +^{n} C_{r - 1} =^{n + 1} C_{r}]$

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

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Similar questions

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

^{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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