Difference between revisions of "2005 AMC 10A Problems/Problem 9"

Revision as of 12:54, 15 January 2020

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

2005 AMC 10A (Problems • Answer Key • Resources)
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All AMC 10 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

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-[[Category:Introductory Number Theory Problems]]
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Difference between revisions of "2005 AMC 10A Problems/Problem 9"

Revision as of 12:54, 15 January 2020

Problem

Solution

See also