If P (n, 4) = 12 . P (n, 2), find n.

P (n, 4) = 12 . P (n, 2)

$\Rightarrow \frac{n !}{(n-4) !}=12 \times \frac{n !}{(n-2) !}$

$\Rightarrow \frac{(n-2) !}{(n-4) !}=12 \times \frac{n !}{n !}$

$\Rightarrow \frac{(n-2)(n-3)(n-4) !}{(n-4) !}=12$

$\Rightarrow(n-2)(n-3)=12$

$\Rightarrow(n-2)(n-3)=4 \times 3$

On comparing the LHS and the RHS, we get :

$n-2=4$

$\Rightarrow n=6$