Question

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

Answer 1

`\tt ^(n)P_(2) = (n \: !)/((n - 2)!) = 20`

`\tt (n(n - 1)(n - 2) \: !)/((n - 2)!) = 20`

`\tt n (n - 1)= 20`

`\tt n^(2) - n - 20 = 0`

`\tt n^(2) - 5n + 4n -20 = 0`

`\tt n(n - 5) + 4(n -5) = 0`

`\tt n = 5 \: or \: n = - 4`

Therefore, value of n = 5.