Question

A class consists of 10 boys and 8 girls. Three students are selected at random. What is the probability that the selected group has  at least one girl?

Answer 1

Total number of students = (10 + 8) = 18
Let S be the sample space.
Then n(S) = number of ways of selecting 3 students out of 18 = ¹⁸C₃ ways 

Probability of at least one girl = 1 -  P(no girl)

                                                = 1 - P(all 3 are boys)

                                               =\[1 - \frac{^{10}{}{C}_3}{^{18}{}{C}_3} = 1 - \frac{5}{34} = \frac{29}{34}\]