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Q.

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

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a

17

b

41

c

38

d

52

answer is C.

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Detailed Solution

$\frac{^{56} p_{r + 6}}{^{54} p_{r + 3}} = \frac{30800}{1}$

$\begin{array}{l} \Rightarrow \frac{(56)!}{(50 - r)!} \times \frac{(51 - r)!}{54!} = 30800 \\ \Rightarrow \frac{56 \times 55 \times 54!}{(50 - r)!} \times \frac{(51 - r) \times (50 - r)!}{54!} = 30800 \\ \Rightarrow 3080 (51 - r) = 30800 \\ \Rightarrow r = 41 \end{array}$

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