If P (n, 5) = 20. P(n, 3), find n
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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