If $^{56} P_{r + 6} :^{54} P_{r + 3}$ = 30800:1, then r =

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Solution

The correct option is B
41

$\frac{56!}{(50 - r)!} \times \frac{(51 - r)!}{54!}$

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

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