GATE 2026 ME – Question 39
A student council of 10 members consists of two students from engineering school, three students from science school and five students from arts school. The university administration selects three students from the council at random. What is the chance that out of the selected students, two belong to the same school and the third belongs to different school?
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Correct answer: (A) 79/120
Explanation
The number of ways to choose 3 of the 10 students is $\binom{10}{3} = 120$. Count the choices with exactly two from the same school: engineering gives $\binom{2}{2} \times 8 = 8$, science gives $\binom{3}{2} \times 7 = 21$, and arts gives $\binom{5}{2} \times 5 = 50$. The total is $8 + 21 + 50 = 79$, so the probability is $\frac{79}{120}$.