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Question
A committee of 4 persons has to be chosen from 8 boys and 6 girls, consisting of at least one girl. Find the probability that the committee consists of more girls than boys.
Solution
Case 1 : 1 girl + 3 boys = ` ""^6C_1 xx ""^8C_3`
Case 2 : 2 girl + 2 boys = ` ""^6C_2 xx ""^8C_2`
Case 3 : 3 girl + 1 boys = ` ""^6C_3 xx ""^8C_1`
Case 4 : 4 girl + 0 boys = ` ""^6C_4 xx ""^8C_0`
Required probability = `( ""^6C_3 xx ""^8C_1)/(""^14C_4) + ( ""^6C_4 xx ""^8C_0)/(""^14C_4)`
= `(160)/(1001) + (15)/(1001) = (175)/(1001)`
= `(25)/(143) = 0.1748`
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