Let the answer be k . We count the total number of paris of students were on duty together in the k days. Since every pair of students was on duty together exactly once, this is equal to \(C^{15}_2\) x 1 = 105. On the other hand, since 3 students were on duty per day, this is also equal to \(C^3_2\) x k = 3k. Hence 3k = 105 and so k = 35