Question

In a class, there are 10 boys and 8 girls. When 3 students are selected at random, the probability that 2 girls and 1 boy are selected, is

• A. \(\frac{35}{102}\)
• B. \(\frac{15}{102}\)
• C. \(\frac{55}{102}\)
• D. \(\frac{25}{102}\)

Hint:

When calculating probabilities with combinations, use the formula \(P = \frac{{favorable outcomes}}{{total outcomes}}\).

Answer 1

The Correct Option is A

To calculate the probability, we use combinations to determine the total number of ways to choose 3 students, as well as the favorable outcomes for choosing 2 girls and 1 boy.

- The total number of ways to choose 3 students from 18 is given by \( \binom{18}{3} \).
- The number of ways to choose 2 girls from 8 is \( \binom{8}{2} \).
- The number of ways to choose 1 boy from 10 is \( \binom{10}{1} \).

Thus, the probability \( P \) is given by the formula: \[ P = \frac{\binom{8}{2} \times \binom{10}{1}}{\binom{18}{3}} = \frac{28 \times 10}{\frac{18 \times 17 \times 16}{3 \times 2 \times 1}} = \frac{35}{102} \] Therefore, the probability is \( \frac{35}{102} \).