The value of $^{10} C_{4} +^{10} C_{5}$ is

462

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466

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469

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465

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Solution

The correct option is B 462
$^{10} C_{4} +^{10} C_{5} =^{11} C_{5}$ since $^{n} C_{r - 1} +^{n} C_{r} =^{n + 1} C_{r}$

$\Rightarrow$ $^{n} C_{r} = \frac{n!}{r! (n - r)!}$

$= \frac{11!}{5! \cdot 6!} = 462$

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