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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

$p = (x + 3) p_{x + 3}, q = (x + 1) p_{11}$

$r = (x - 10)! and$

$p = 182 q r$

$(x + 3)! = 182 \times \frac{(x + 1)!}{(x - 10)!} \times (x - 10)!$

$(x + 3) (x + 2) = 14 \times 13 \Rightarrow x + 3 = 14$

$\Rightarrow x = 11$

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