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  4. If nP4 = 5 (nP3), then the value of n is equal to

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Q. If $^n$P$_4$ = $5$ ($^nP_3$), then the value of $n$ is equal to

KEAMKEAM 2016Permutations and Combinations

Solution:

Given, ${ }^{n} P_{4}=5\left({ }^{n} P_{3}\right)$
$\Rightarrow \frac{n !}{(n-4) !}=\frac{5 \times n !}{(n-3) !}$
$\Rightarrow \frac{n !}{(n-4) !}=\frac{5 \times n !}{(n-3)(n-4) !}$
$\Rightarrow n-3=5 \Rightarrow n=8$