QA – Placement Quizzes | Permutation and Combination | Question 9

Out of 7 boys and 4 girls, how many queues of 3 boys and 2 girls can be formed?
(A) 120
(B) 25200
(C) 24800
(D) 1440


Answer: (B)

Explanation: Number of ways to choose 3 boys out of 7 = ⁷C₃.
Number of ways to choose 2 girls out of 4 = ⁴C₂.
Therefore, number of ways to choose the required groups = ⁷C₃ * ⁴C₂ = 35 * 6 = 210.
Number of ways to arrange the 3 boys and 2 girls in a queue = 5! = 120.
Therefore, the required number of queues = 210 * 120 = 25200.

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