If n items are arranged two at a time, the number obtained is 20. Find…

If n items are arranged two at a time, the number obtained is 20. Find the value of n.

Correct Answer: Option A

Explanation

(^{n}P_{2} = frac{n!}{(n – 2)!} = 20 )

(frac{n(n – 1)(n – 2)!}{(n – 2)!} = 20)

(n(n – 1) = 20 implies n^{2} – n – 20 = 0)

(n^{2} – 5n + 4n – 20 = 0)

(n(n – 5) + 4(n – 5) = 0)

(n = text{5 or -4})

(n = 5)