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Ratio and Proportion

If 22 C r i...

Question

If ${^{22} C}_{r}$ is the largest binomial coefficient in the expansion of ${(1 + x)}^{22}$ , find the value of ${^{13} C}_{r}$ .

24

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65

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26

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78

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Solution

The correct option is D $78$
Fact: If $n$ is even, then greatest coefficient in the expansion of $(1 + x)^{n}$ is $^{n} C_{\frac{n}{2}}$
Here $n = 22$ , so greatest coefficient in the expansion of $(1 + x)^{22}$ is $^{22} C_{11}$ , so $r = 11$

Therefore $^{13} C_{r} =^{13} C_{11} = 78$

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