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

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==Solution==
 
==Solution==
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There are <math>\frac{5!}{2!3!}=10</math> distinct arrangments of three <math>X</math>'s and two <math>O</math>'s.  
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There are <math>\frac{5!}{2!3!}=10</math> distinct arrangements of three <math>X</math>'s and two <math>O</math>'s.  
  
 
There is only <math>1</math> distinct arrangement that reads <math>XOXOX</math>
 
There is only <math>1</math> distinct arrangement that reads <math>XOXOX</math>
  
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Therfore the desired [[probability]] is <math>\frac{1}{10} \Rightarrow \mathrm{(B)}</math>
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Therefore the desired [[probability]] is <math>\frac{1}{10} \Rightarrow \mathrm{(B)}</math>
  
 
==See Also==
 
==See Also==

Revision as of 00:50, 27 November 2007

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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