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Question: If \(nP_{5} = 9 \times^{n - 1}P_{4}\), then the value of \(n\) is....

If nP5=9×n−1P4nP_{5} = 9 \times^{n - 1}P_{4}, then the value of nn is.

A

6

B

8

C

5

D

9

Answer

9

Explanation

Solution

nP5n−1P4=9⇒n!(n−5)!×(n−5)!(n−1)!=9⇒n=9\frac{nP_{5}}{n - 1P_{4}} = 9 \Rightarrow \frac{n!}{(n - 5)!} \times \frac{(n - 5)!}{(n - 1)!} = 9 \Rightarrow n = 9.