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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?
Solution
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 =\[\frac{^{10}{}{C}_3}{^{18}{}{C}_3} = \frac{10 \times 9 \times 8}{18 \times 17 \times 16} = \frac{5}{34}\]
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