2005 AMC 10A Problems/Problem 9

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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 $XOXOX$ ?

$\mathrm{(A) \ } \frac{1}{12}\qquad \mathrm{(B) \ } \frac{1}{10}\qquad \mathrm{(C) \ } \frac{1}{6}\qquad \mathrm{(D) \ } \frac...$

Solution

There are $\frac{5!}{2!3!}=10$ distinct arrangements of three $X$ 's and two $O$ 's.

There is only $1$ distinct arrangement that reads $XOXOX$

Therefore the desired probability is $\frac{1}{10} \Rightarrow \mathrm{(B)}$

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2005 AMC 10A Problems/Problem 9

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