(B) Given the ratio: $\frac{^{56}P_{r+6}}{^{54}P_{r+3}} = 30800$Using the formula $^nP_r = \frac{n!}{(n-r)!}$,we have:$\frac{56!}{(56-(r+6))!} \times

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(B) Given the ratio: $\frac{^{56}P_{r+6}}{^{54}P_{r+3}} = 30800$Using the formula $^nP_r = \frac{n!}{(n-r)!}$,we have:$\frac{56!}{(56-(r+6))!} \times \frac{(54-(r+3))!}{54!} = 30800$$\frac{56!}{(50-r)!} \times \frac{(51-r)!}{54!} = 30800$$\frac{56 \times 55 \times 54!}{54!} \times \frac{(51-r) \times (50-r)!}{(50-r)!} = 30800$$56 \times 55 \times (51-r) = 30800$$3080 \times (51-r) = 30800$$51-r = 10$$r = 41$

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

Medium

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

A
$31$
B
$41$
C
$51$
D
None of these

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

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If $^n{P_r} = 720 \times {^n{C_r}}$,then $r$ is equal to:

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