(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 Permutations and Combinations 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 Questions

Class 11

Mathematics Questions

Chapter

Permutations and Combinations

Subtopic

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

$A$ library has $a$ copies of one book,$b$ copies of each of two books,$c$ copies of each of three books,and single copies of $d$ books. The total number of ways in which these books can be arranged is:

Medium

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How many words can be formed using the letters of the word $BHARAT$ such that $B$ and $H$ never come together?

Medium

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

Medium

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The number of $4$-letter words, with or without meaning, each consisting of two vowels and two consonants that can be formed from the letters of the word $INCONSEQUENTIAL$, without repeating any letter, is:

DifficultJEE MAIN 2026

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How many $3$-digit numbers can be formed by using the digits $1$ to $9$ if no digit is repeated?

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

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$A$ library has $a$ copies of one book,$b$ copies of each of two books,$c$ copies of each of three books,and single copies of $d$ books. The total number of ways in which these books can be arranged is:

How many words can be formed using the letters of the word $BHARAT$ such that $B$ and $H$ never come together?

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

The number of $4$-letter words, with or without meaning, each consisting of two vowels and two consonants that can be formed from the letters of the word $INCONSEQUENTIAL$, without repeating any letter, is:

How many $3$-digit numbers can be formed by using the digits $1$ to $9$ if no digit is repeated?

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