2. 15 students join a summer course. Every day, 3 students are on duty after school to clean the classroom. After the course, it was found that every pair of students have been on duty together exactly once. How many days does the course last for?
(1 mark)
2. 15 students join a summer course. Every day, 3 students are on duty after school to clean the classroom. After the course, it was found that every pair of students have been on duty together exactly once. How many days does the course last for?
(1 mark)
2. 35
2. Every day $C_{3}^{2}=3$ pairs of students are on duty. Altogether $C_{15}^{2}=105$ pairs of students have been on duty. Therefore the answer is $105 \div 3=35$.