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If n items are arranged two at a time, the number obtaine...

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

A.

5

B.

10

C.

15

D.

40

Correct answer is A

nP2=n!(n2)!=20

n(n1)(n2)!(n2)!=20

n(n1)=20n2n20=0

n25n+4n20=0

n(n5)+4(n5)=0

n=5 or -4

n=5