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

1280

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1440

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1520

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1640

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Solution

The correct option is D $1640$
We have:
$\frac{56!}{(50 - r)!} . \frac{(51 - r)!}{54!} = 30800 => 56.55. (51 - r) = 30800 => 51 - r = 10 => r = 41$
Therefore, $_{2}^{r} P =_{2}^{41} P = 41.40 = 1640$
Hence, (D) is correct.

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