• # question_answer If  $^{56}{{P}_{r+6}}{{:}^{54}}{{P}_{r+3}}=30800:1$, then $r=$ [Roorkee 1983; Kurukshetra CEE 1998] A) 31 B) 41 C) 51 D) None of these

Correct Answer: B

Solution :

$\frac{56\ !}{(50-r)\ !}\times \frac{(51-r)\ !}{54\ !}$ $=\frac{30800}{1}\Rightarrow 56\times 55\times (51-r)=30800$ $\Rightarrow$$r=41$.

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