Question:
If ${ }^{n} P_{4}=360$, find the value of $n .$
Solution:
${ }^{n} P_{4}=360$
$\Rightarrow \frac{n !}{(n-4) !}=360$
$\Rightarrow \frac{n(n-1)(n-2)(n-3)(n-4) !}{(n-4) !}=360$
$\Rightarrow n(n-1)(n-2)(n-3)=360$
$\Rightarrow n(n-1)(n-2)(n-3)=6 \times 5 \times 4 \times 3$
On comparing the two sides, we get:
$n=6$