A committee of 4 students is selected at random from a grourp consisting of 8 boys and 4 girls. Given that there is at least one girl in the committee, calculate the probability that there are exactly 2 girls in the committee.

Explanation

No. of ways at least one girl`=text(Total-(none of the selected members is a girl))`
`=(12C)_4-(8C)_4`
`=(12xx11xx10xx9)/(4xx3xx2xx1)-(8xx7xx6xx5)/(4xx3xx2xx1)`
`495-70=425`
No. of ways of selecting exactly 2 girls`=(8C)_2+(4C)_2`
`=(8xx7)/2xx(4xx3)/2=168`
Probability`=168/425`