Question:
If P (n, 4) = 12 . P (n, 2), find n.
Solution:
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 :
$n-2=4$
$\Rightarrow n=6$
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