JAMB 2024 Mathematics · Question 45

From a class of 5 girls and 7 boys, a committee consisting of 2 girls and 3 boys is to be formed. How many ways can this be done?

Options

A.350 ways
B.420 ways
C.550 ways
D.720 ways

Answer: A. 350 ways

Explanation written with AI and checked against the answer key

Analyze the question We need to choose 2 girls from 5 AND 3 boys from 7. Order doesn't matter in a committee, so we use combinations. Since both selections must happen together, we multiply. Concept The number of ways to choose r items from n is: ⁿCᵣ = n! / [r!(n − r)!] "AND" means multiply the number of ways. Solution Girls: ⁵C₂ = (5 × 4) / (2 × 1) = 10 Boys: ⁷C₃ = (7 × 6 × 5) / (3 × 2 × 1) = 210 / 6 = 35 Total ways = ⁵C₂ × ⁷C₃ = 10 × 35 = 350 Answer: A. 350 ways Tip: In "choose from group 1 AND group 2" questions, find each combination separately and multiply. Use ⁿCᵣ whenever order does not matter (committees, teams, selections), and use permutations only when arrangement or position matters (e.g., president, secretary, treasurer).

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