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 girls?

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 eight girls, three girls can be selected in ⁸C₃ ways.
∴ Favourable number of events, n(E) = ⁸C₃
Hence, required probability =\[\frac{^{8}{}{C}_3}{^{18}{}{C}_3} = \frac{8 \times 7 \times 6}{18 \times 17 \times 16} = \frac{7}{102}\]