Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# 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? - Mathematics

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?

#### 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

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

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 33 Probability
Exercise 33.3 | Q 38.3 | Page 47