AMC10 2005 10A, Problem 9

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 $\frac{5!}{2!3!}=10$ distinct arrangements of three $X$'s and two $O$'s. There is only $1$ distinct arrangement that reads $XOXOX$. Therefore the desired probability is $\fbox{\frac{1}{10}}$

Answer: \frac{1}{10}