(B) Given: ${}^n{P_5} = 20 \times {}^n{P_3}$Using the formula ${}^n{P_r} = \frac{n!}{(n-r)!}$,we have:$\frac{n!}{(n-5)!} = 20 \times \frac{n!}{(n-3)!}

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(B) Given: ${}^n{P_5} = 20 \times {}^n{P_3}$Using the formula ${}^n{P_r} = \frac{n!}{(n-r)!}$,we have:$\frac{n!}{(n-5)!} = 20 \times \frac{n!}{(n-3)!}$Dividing both sides by $n!$ (since $n! \neq 0$):$\frac{1}{(n-5)!} = \frac{20}{(n-3)(n-4)(n-5)!}$$\frac{1}{1} = \frac{20}{(n-3)(n-4)}$$(n-3)(n-4) = 20$$n^2 - 7n + 12 = 20$$n^2 - 7n - 8 = 0$$(n-8)(n+1) = 0$Since $n$ must be a positive integer and $n \geq 5$,we have $n = 8$.

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

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If ${}^n{P_5} = 20 \times {}^n{P_3}$,then $n = $

A
$4$
B
$8$
C
$6$
D
$7$

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Class 11

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Permutation and Combination

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

The number of ways of arranging $8$ boys and $8$ girls in a row so that boys and girls sit alternately is

MediumTS EAMCET 2018

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MediumMHT CET 2024

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How many words,with or without meaning,each of $3$ vowels and $2$ consonants can be formed from the letters of the word $INVOLUTE$?

Medium

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What is the number of permutations of three letters $A, B, C$ taken all at a time?

Easy

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Eight different letters of an alphabet are given. Words of four letters from these are formed. The number of such words with at least one letter repeated is:

MediumTS EAMCET 2006

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If ${}^n{P_5} = 20 \times {}^n{P_3}$,then $n = $

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The number of ways of arranging $8$ boys and $8$ girls in a row so that boys and girls sit alternately is

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