UPSC NDA Math Model Paper 3

From n socks, 2 can be chosen in C(n, 2) ways.
From 3 red socks, 2 can be chosen in C(3, 2) ways
Probability that both socks selected are red
=

C(3,2)

C(n,2)

=

6

n(n−1)

It is given that Probability that both socks selected are red =

1

2

⇒

6

n(n−1)

=

1

2

⇒n2−n−12=0
⇒(n−4)(n+3)=0
⇒n=4,−3
n cannot be negative so, n = 4.
Correct option is (2).