The 15 animators go on a training session together. Each day, 3 animators supervise the pool. It is noted that each pair of animators has supervised the pool together exactly once. How many days will the training session last?
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a pair of animathors monitored the pool together only once, so $\binom{15}{2}$ pairs of animathors have monitored the pool together. Each day, since 3 animathors monitor the pool, $\binom{3}{2}$ pairs of animathors monitor the pool together, and each day these pairs are distinct. In particular, over the $N$ days, $N \times \binom{3}{2}$ pairs of animathors have monitored the pool together. Therefore, we have $N \times \binom{3}{2} = \binom{15}{2}$, which gives $N = \frac{\binom{15}{2}}{\binom{3}{2}} = 35$.