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nCr Definitions and Properties

If nC15 = n...

Question

If $^{n} C_{15} =^{n} C_{8}$ , then the value of $^{n} C_{21}$ is

254

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250

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253

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None of these

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Solution

The correct option is C $253$
Given, $^{n} C_{15} =^{n} C_{8}$
$\Rightarrow^{n} C_{n - 15} =^{n} C_{8}$
$∴ n - 15 = 8 \Rightarrow n = 23$
Now, $^{n} C_{21} =^{23} C_{21}$
$= \frac{(23)!}{2! \times (21)!}$
$= \frac{23 \times 22}{2} = 23 \times 11 = 253$ .

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