UPSC NDA Math Model Paper 6

The total number of caps = 2 + 4 + 5 + 1 = 12
The number of ways for selecting four caps =12C1
The total number of caps other than green = 12 - 5 = 7
The number of ways for selecting four caps other than green =‌7C4
The probability of selecting four caps and none of them are green ⇒P(A′)=

‌7C4

‌2C4

⇒P(A′)=

7!(12−4)!4!

4!(7−4)!12!

⇒P(A′)=

7

99