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jmc

counting and probability senior

Problem

Ten people are sitting around a round table. Three of them are chosen at random to give a presentation. What is the probability that the three chosen people were sitting in consecutive seats?
Solution
Let's count as our outcomes the ways to select 3 people without regard to order. There are ways to select any 3 people. The number of successful outcomes is the number of ways to select 3 consecutive people. There are only 10 ways to do this -- think of first selecting the middle person, then we take his or her two neighbors. Therefore, the probability is .
Final answer
\frac{1}{12}