Question:
If P (n, 5) = 20. P(n, 3), find n
Solution:
P (n, 5) = 20. P(n, 3)
$\Rightarrow \frac{n !}{(n-5) !}=20 \times \frac{n !}{(n-3) !}$
$\Rightarrow \frac{n !}{n !}=20 \times \frac{(n-5) !}{(n-3) !}$
$\Rightarrow 1=20 \times \frac{(n-5) !}{(n-3)(n-4)(n-5) !}$
$\Rightarrow(n-3)(n-4)=20$
$\Rightarrow(n-3)(n-4)=5 \times 4$
On comparing the two sides, we get:
$\Rightarrow n-3=5$
$\Rightarrow n=8$
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