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2005 AMC 10A Problem 9

Problem 9 of 25EasierCounting & Probability

Three tiles are marked X and two other tiles are marked O. The five tiles are randomly arranged in a row. What is the probability that the arrangement reads XOXOX?

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Solution

The three X positions can be any of (53)=10\binom{5}{3} = 10 equally likely choices, and exactly one of them produces XOXOX. So the probability is 110.\dfrac{1}{10}. Thus, the correct answer is B.

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Concepts: basic probability · combinations

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.