(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 Questions

Class 11

Mathematics Questions

Chapter

Permutation and Combination

Subtopic

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

How many numbers less than $10000$ can be formed using the eight digits $1, 2, 3, 4, 5, 6, 7, 0$? (Repetition of digits is allowed)

Medium

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The number of words which can be made out of the letters of the word $MOBILE$ when consonants always occupy odd places is

Medium

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The number of different words that can be formed out of the letters of the word $MORADABAD$ taken four at a time is

Difficult

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Find the value of $n$ such that $^{n}P_{5} = 42 \, ^{n}P_{3}$,where $n > 4$.

Medium

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In how many ways can $6$ examination papers be arranged so that the best and the worst papers are never together?

Difficult

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

Similar Questions

How many numbers less than $10000$ can be formed using the eight digits $1, 2, 3, 4, 5, 6, 7, 0$? (Repetition of digits is allowed)

The number of words which can be made out of the letters of the word $MOBILE$ when consonants always occupy odd places is

The number of different words that can be formed out of the letters of the word $MORADABAD$ taken four at a time is

Find the value of $n$ such that $^{n}P_{5} = 42 \, ^{n}P_{3}$,where $n > 4$.

In how many ways can $6$ examination papers be arranged so that the best and the worst papers are never together?

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