There are ten meerkats in a colony. Every night, three meerkats stand guard while the others sleep. During a certain period of nights, every group of three meerkats has stood guard exactly once. During that period, how many nights of sleep does each meerkat get?
+23 There are \(\binom{10}{3} = 120 \) different combinations of 3 meerkats that have to stand guard. Therefore each meerkat has to stand guard \(\frac{120}{10} = 12 \) nights. That means each meerkat gets 108 nights of sleep.
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