SOLUTION: From a group of 10 boys and 12 girls, a committee of 4 students is chosen at random. How many four-person committees containing at least 1 girl are possible?

Question 365753: From a group of 10 boys and 12 girls, a committee of 4 students is chosen at random. How many four-person committees containing at least 1 girl are possible?
Answer by sudhanshu_kmr(1152) (Show Source): You can put this solution on YOUR website!

here we have to find no. of groups in which at least one girl

i.e from total no. of groups discard those groups in which only boys.

no. of ways to selecting 4 from total 22 = 22C4

no. of ways to selecting 4 boys from total 10 boys = 10C4

total possible ways = 22C4 - 10C4 = 7315 - 210 = 7105

answer is: 7105

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