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

Asked by Aaryan | 2 years ago |  44

Solution :-

Given:

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

By using the formula,

P (n, r) =$$\dfrac{ n!}{r!(n – r)!}$$

P (n, 4) = $$\dfrac{ n!}{r!(n – 4)!}$$

P (n, 2) =$$\dfrac{ n!}{r!(n – 2)!}$$

So, from the question,

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

Substituting the obtained values in above expression we get,

$$\dfrac{ n!}{(n – 4)!} = 12 × \dfrac{n!}{(n – 2)!}$$

Upon evaluating,

(n – 2) (n – 3) = 12

n2 – 3n – 2n + 6 = 12

n2 – 5n + 6 – 12 = 0

n2 – 5n – 6 = 0

n2 – 6n + n – 6 = 0

n (n – 6) – 1(n – 6) = 0

(n – 6) (n – 1) = 0

n = 6 or 1

For, P (n, r): n ≥ r

n = 6 [for, P (n, 4)]

Answered by Aaryan | 2 years ago

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