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counting and probability intermediate
Problem
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?
Solution
There are three X's and two O's, and the tiles are selected without replacement, so the probability is OR
The three tiles marked X are equally likely to lie in any of positions, so the probability of this arrangement is .
The three tiles marked X are equally likely to lie in any of positions, so the probability of this arrangement is .
Final answer
\frac{1}{10}