In a class with 15 boys and 10 girls, three students are chosen at random. What is the probability that exactly 1 girl and 2 boys are chosen?

Given data

• Boys = 15, Girls = 10, Total = 25.
• Selection size = 3; event = exactly 1 girl and 2 boys.

Concept/Approach
Use combinations without replacement: favorable ways ÷ total ways.

Step-by-Step calculation
Total ways = C(25, 3) = 25 × 24 × 23 ÷ 6 = 2300 Favorable ways = C(10, 1) × C(15, 2) = 10 × 105 = 1050 Probability = 1050 ÷ 2300 = 105 ÷ 230 = 21 ÷ 46

Verification/Alternative
Hypergeometric check: P = (10÷25) × (15÷24) × (14÷23) × 3 (for the three placements of the girl) simplifies to 21÷46.

Common pitfalls

• Choosing 2 girls and 1 boy by mistake.
• Using permutations instead of combinations.

Final Answer
21/46