(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

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

A
$4$
B
$5$
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

If all the letters of the word $MOST$ are permuted and the words (with or without meaning) thus obtained are arranged in the dictionary order,then the rank of the word $STOM$ when counted from the rank of the word $MOST$ is:

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How many numbers lying between $99$ and $1000$ can be formed using the digits $2, 3, 7, 0, 8, 6$ if each digit is used only once in each number?

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How many numbers between $999$ and $10,000$ can be formed using the digits $0, 2, 3, 6, 7, 8$ without repetition?

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From a committee of $8$ persons,in how many ways can we choose a chairman and a vice chairman assuming one person cannot hold more than one position?

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The number of $3$ digit odd numbers that can be formed by using the digits $1, 2, 3, 4, 5, 6$ when the repetition of digits is allowed is:

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

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If all the letters of the word $MOST$ are permuted and the words (with or without meaning) thus obtained are arranged in the dictionary order,then the rank of the word $STOM$ when counted from the rank of the word $MOST$ is:

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