(D) The given equation is ${}^{27}P_{r+7} = 7722 \times {}^{25}P_{r+4}$.Using the formula ${}^{n}P_{r} = \frac{n!}{(n-r)!}$,we have:$\frac{27!}{(27-(r

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(D) The given equation is ${}^{27}P_{r+7} = 7722 \times {}^{25}P_{r+4}$.Using the formula ${}^{n}P_{r} = \frac{n!}{(n-r)!}$,we have:$\frac{27!}{(27-(r+7))!} = 7722 \times \frac{25!}{(25-(r+4))!}$$\frac{27!}{(20-r)!} = 7722 \times \frac{25!}{(21-r)!}$$\frac{27 \times 26 \times 25!}{(20-r)!} = 7722 \times \frac{25!}{(21-r)(20-r)!}$$27 \times 26 = \frac{7722}{21-r}$$702 = \frac{7722}{21-r}$$21-r = \frac{7722}{702} = 11$$r = 21 - 11 = 10$.Thus,$r = 10$.

Class 11 Mathematics Permutations and Combinations Definition of permutation, Number of permutations with or without repetition, Conditional permutations

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If ${}^{27}P_{r+7} = 7722 \times {}^{25}P_{r+4}$,then $r = $

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$9$
B
$12$
C
$11$
D
$10$

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Permutations and Combinations

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Definition of permutation, Number of permutations with or without repetition, Conditional permutations

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If ${}^{27}P_{r+7} = 7722 \times {}^{25}P_{r+4}$,then $r = $

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