Answer:
[tex]\tt ^{n}P_{2} = \dfrac{n \: !}{(n - 2)!} = 20[/tex]
[tex]\tt \dfrac{n(n - 1)(n - 2) \: !}{(n - 2)!} = 20[/tex]
[tex] \tt n (n - 1)= 20[/tex]
[tex]\tt n^{2} - n - 20 = 0[/tex]
[tex]\tt n^{2} - 5n + 4n -20 = 0[/tex]
[tex]\tt n(n - 5) + 4(n -5) = 0[/tex]
[tex]\tt n = 5 \: or \: n = - 4[/tex]
Therefore, value of n = 5.
