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Q)

Evaluate $\large\frac{n!}{(n-r)!}$ when n=9,r=5

$\begin{array}{1 1}(A)\;15100\\(B)\;15110\\(C)\;15130\\(D)\;15120\end{array} $

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A)
Given :$\large\frac{n!}{(n-r)!}$
$n=9,r=5$
$\large\frac{n!}{(n-r)!}=\frac{9!}{(9-5)!}$
$\Rightarrow \large\frac{9!}{4!}$
$\Rightarrow \large\frac{9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{4!\times 3\times 2\times 1}$
$\Rightarrow 9\times 8\times 7\times 6\times 5$
$\Rightarrow 15120$
Hence (D) is the correct answer.
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