question is of probability

Question

a committee of 4 members is to be formed from 15 boys and 3 girls. find probability that it contains a particular girl

Answer 1

I assume the question asks, find the probability that the committee of 4 contains a girl.

Find first the probability that no member is a girl and then find the complement:

P(girl) = 1 - P(no girls) = 1 - 15C4 / 18C4 = 1 - (14 * 13 * 12) / (18 * 17 * 16) = 1 - 2184 / 4896 = 1 - 0.446 = 0.554

where C is the formula for combination: C (n,r) = n! / r! (n-r)!