(A) Given the equation $\frac{^{n}P_{4}}{^{n-1}P_{4}} = \frac{5}{3}$.Using the formula $^{n}P_{r} = \frac{n!}{(n-r)!}$,we have:$\frac{\frac{n!}{(n-4)!

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(A) Given the equation $\frac{^{n}P_{4}}{^{n-1}P_{4}} = \frac{5}{3}$.Using the formula $^{n}P_{r} = \frac{n!}{(n-r)!}$,we have:$\frac{\frac{n!}{(n-4)!}}{\frac{(n-1)!}{(n-5)!}} = \frac{5}{3}$.This simplifies to $\frac{n \times (n-1)!}{(n-4) \times (n-5)!} \times \frac{(n-5)!}{(n-1)!} = \frac{5}{3}$.$\frac{n}{n-4} = \frac{5}{3}$.Cross-multiplying gives $3n = 5(n-4)$.$3n = 5n - 20$.$2n = 20$.$n = 10$.

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

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Find the value of $n$ such that $\frac{^{n}P_{4}}{^{n-1}P_{4}} = \frac{5}{3}$,where $n > 4$.

A
$10$
B
$12$
C
$8$
D
$15$

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Permutation and Combination

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

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Find the value of $n$ such that $\frac{^{n}P_{4}}{^{n-1}P_{4}} = \frac{5}{3}$,where $n > 4$.

Similar Questions

If all the words with or without meaning made using all the letters of the word $KANPUR$ are arranged as in a dictionary,then the word at $440^{th}$ position in this arrangement is:

If ${}^n P_r = {}^{(n-1)} P_r + x \cdot {}^{(n-1)} P_{(r-1)}$,$\forall n, r \in N$ and $r \leq n$,then $x =$

Find $n$ if $^{n-1}P_{3} : ^{n}P_{4} = 1 : 9$.

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