UPSC NDA Math Model Paper 9

we are picking the four balls without replacement and that the 4 white and 4 red balls are the only balls in the box and that we choose 2 red balls and 2 white balls.
Number of ways to choose 4 balls out of 8=8C4=

8!

4!4!

=70
Number of ways to pick 2 red balls out of 4=4C2=

4!

2!2!

=6
Number of ways to pick 2 white balls out of 4=4C2=

4!

2!2!

=6
Probability =

6×6

70

=

36

70

=

18

35