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 1 boys and 2 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

One boy and two girls can be selected in ¹⁰C₁ × ⁸C₂.
∴ Favourable number of events = ¹⁰C₁ × ⁸C₂
Hence, required probability =\[\frac{^{10}{}{C}_1 \times ^{8}{}{C}_2}{^{18}{}{C}_3} = \frac{10 \times 28}{816} = \frac{35}{102}\]