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If p denotes the number of permutations of $(x + 3)$ things taken all at a time, q denotes the number of permutations of $(x + 1)$ things taken 11 at a time and r denotes the number of permutations of $(x - 10)$ things taken all at a time such that $p = 182$ qr, then the value of x is

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answer is B.

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Detailed Solution

$\begin{array}{l} p = (x + 3) p_{x + 3}, q = (x + 1) p_{11} \\ r = (x - 10)! and p = 182 qr \Rightarrow (x + 3)! = 182 \frac{(x + 1)!}{(x - 10)!} \end{array} (x - 10)! \Rightarrow x = 11$

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