AP EAMCET · Maths · Probability
A class has fifteen boys and five girls. Suppose three students are selected at random from the class. The probability that there are two boys and one girl is
- A \(\frac{35}{76}\)
- B \(\frac{35}{38}\)
- C \(\frac{7}{76}\)
- D \(\frac{35}{72}\)
Answer & Solution
Correct Answer
(A) \(\frac{35}{76}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} \therefore \text { Required probability } & =\frac{{ }^{15} C_2 \times{ }^5 C_1}{{ }^{20} C_3} \\ & =\frac{15 \times 7 \times 5}{\frac{20 \times 19 \times 18}{3 \times 2}} \\ & =\frac{7 \times 25}{20 \times 19}=\frac{35}{76}\end{aligned}\)
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