# If P (N, 5) = 20. P(N, 3), Find N ? - Mathematics

If P (n, 5) = 20. P(n, 3), find n ?

#### Solution

P (n, 5) = 20. P(n, 3)

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

Concept: Factorial N (N!) Permutations and Combinations
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 16 Permutations
Exercise 16.3 | Q 4 | Page 28