Solve the following
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:

$n=6$