(C) Given the ratio $^nP_4 : ^nP_5 = 1 : 2$. Using the formula $^nP_r = \frac{n!}{(n-r)!}$,we have: $\frac{n!}{(n-4)!} \div \frac{n!}{(n-5)!} = \frac{

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(C) Given the ratio $^nP_4 : ^nP_5 = 1 : 2$. Using the formula $^nP_r = \frac{n!}{(n-r)!}$,we have: $\frac{n!}{(n-4)!} \div \frac{n!}{(n-5)!} = \frac{1}{2}$ $\frac{n!}{(n-4)!} \times \frac{(n-5)!}{n!} = \frac{1}{2}$ $\frac{(n-5)!}{(n-4)(n-5)!} = \frac{1}{2}$ $\frac{1}{n-4} = \frac{1}{2}$ $n - 4 = 2$ $n = 6$

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

Easy

If $^nP_4 : ^nP_5 = 1 : 2$,then $n = \dots$

A
$4$
B
$5$
C
$6$
D
$7$

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Class 11

Mathematics Questions

Chapter

Permutation and Combination

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

How many numbers less than $1000$ can be formed using the digits $0, 1, 2, 4,$ and $5$ if repetition of digits is not allowed?

Medium

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There are $3$ candidates for a post and one is to be selected by the votes of $7$ men. The number of ways in which votes can be given is

Easy

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The letters of the word $OUGHT$ are written in all possible ways and these words are arranged as in a dictionary,in a series. Then the serial number of the word $TOUGH$ is :

DifficultJEE MAIN 2023

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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 $DAUGHTER$?

EasyAP EAMCET 2022

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The number of ways in which all the letters of the word $COMBINATION$ can be arranged so that the vowels always come together is:

MediumAP EAMCET 2018

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If $^nP_4 : ^nP_5 = 1 : 2$,then $n = \dots$

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How many numbers less than $1000$ can be formed using the digits $0, 1, 2, 4,$ and $5$ if repetition of digits is not allowed?

There are $3$ candidates for a post and one is to be selected by the votes of $7$ men. The number of ways in which votes can be given is

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