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Revision as of 10:29, 4 July 2013

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 $XOXOX$?

$\mathrm{(A) \ } \frac{1}{12}\qquad \mathrm{(B) \ } \frac{1}{10}\qquad \mathrm{(C) \ } \frac{1}{6}\qquad \mathrm{(D) \ } \frac{1}{4}\qquad \mathrm{(E) \ } \frac{1}{3}$

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 $\frac{1}{10} \Rightarrow \mathrm{(B)}$

See Also

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