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

Explanation

let event of getting atleast one girl in committee be`A`

A= 1 girl + 2 girl + 3 girl + 4 girl

`= .^12C_4 - .^8C_4 `

`= (12 xx 11xx 10 xx 9)/(4 xx 3 xx2) - ( 8 xx7 xx 6 xx 5)/(4 xx 3 xx 2 xx1)`

`= 495- 70 = 425`

let B be the event of exactly 2 girls in the committee

`B= .^4C_2 .^8C_2`

`= (4 xx 3)/2 xx( 8 xx7)/2`

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