3 students are selected from a class that has 10 boys and 5

3 students are selected from a class that has 10 boys and 5 girls. What is the probability that 1 boy and 2 girls are selected?

Solution

The class has 15 students of which 10 are boys and 5 are girls.   Three students are selected (at random).

We further assume that the selection is made by SRSWOR.

Total number of ways in which 3 students can be selected from 15 students is 15 C 3 = (15*14*13)/ 3! = 455.

Again, 1 boy can be selected from 10 boys in 10C1 = 10 ways. Also, 2 girls can be selected from 5 girls in 5C2 = 10 ways. By multiplication principle, the combined event can occur in 10*10 = 100 ways.

By using classical definition of probability, the required probability is 100 / 455 = 20 / 91.