(C) Given the equation: $\frac{^{56}P_{r+6}}{^{54}P_{r+3}} = 30800$Using the formula $^nP_r = \frac{n!}{(n-r)!}$,we get:$\frac{56!}{(56-(r+6))!} \time

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

Class 11 Mathematics Permutation and Combination Definition of permutation, Number of permutations with or without repetition, Conditional permutations

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If $\frac{^{56}P_{r+6}}{^{54}P_{r+3}} = 30800$,then $r = \dots$

A
$21$
B
$31$
C
$41$
D
$51$

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Class 11

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Chapter

Permutation and Combination

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

If all the digits in the number $53426$ are permuted in all possible ways and are arranged in decreasing order,then the number having rank $89$ is:

MediumAP EAMCET 2018

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The number of natural numbers less than $500$ in which no two digits are repeated is

EasyAP EAMCET 2023

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In how many ways can $mn$ letters be posted in $n$ letter-boxes?

Difficult

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The number of ways of arranging the letters of the word $LINEAR$ so that the letters $N$ and $R$ do not come together and $E$ and $A$ come together is

MediumTS EAMCET 2022

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$A$ three-digit number $n$ is such that the last two digits are equal and differ from the first digit. The number of such $n$'s is:

EasyTS EAMCET 2005

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If $\frac{^{56}P_{r+6}}{^{54}P_{r+3}} = 30800$,then $r = \dots$

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If all the digits in the number $53426$ are permuted in all possible ways and are arranged in decreasing order,then the number having rank $89$ is:

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