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  all boys?

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

Out of 10 boys, three boys can be selected in ¹⁰C₃ ways.
∴ Favourable number of events, n(E) = ¹⁰C₃
Hence, required probability =\[\frac{^{10}{}{C}_3}{^{18}{}{C}_3} = \frac{10 \times 9 \times 8}{18 \times 17 \times 16} = \frac{5}{34}\]