(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

Easy

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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Chapter

Permutation and Combination

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

How many $6$-digit numbers can be formed using the digits of the number $112233$?

Easy

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There are $6$ periods in each working day of a school. The number of ways one can arrange $5$ subjects such that each is allowed at least one period is:

MediumMHT CET 2022

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Let $n$ be a number of digits. Using the three digits $2, 5, 7$,at least $900$ distinct $n$-digit numbers can be formed. What is the minimum value of $n$?

Medium

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How many numbers between $5000$ and $10000$ can be formed using the digits $1, 2, 3, 4, 5, 6, 7, 8, 9$ if no digit is repeated?

Medium

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The number of words,with or without meaning,that can be formed using all the letters of the word $ASSASSINATION$ so that the vowels occur together,is $.............$.

DifficultJEE MAIN 2023

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

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How many $6$-digit numbers can be formed using the digits of the number $112233$?

There are $6$ periods in each working day of a school. The number of ways one can arrange $5$ subjects such that each is allowed at least one period is:

Let $n$ be a number of digits. Using the three digits $2, 5, 7$,at least $900$ distinct $n$-digit numbers can be formed. What is the minimum value of $n$?

How many numbers between $5000$ and $10000$ can be formed using the digits $1, 2, 3, 4, 5, 6, 7, 8, 9$ if no digit is repeated?

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