Difference between revisions of "University of South Carolina High School Math Contest/1993 Exam/Problem 11"

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The probability is <math>\frac{3!+2!+1!}{4!}=\frac{3}{8}</math>.
 
The probability is <math>\frac{3!+2!+1!}{4!}=\frac{3}{8}</math>.
  
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Revision as of 17:18, 17 August 2006

Problem

Suppose that 4 cards labeled 1 to 4 are placed randomly into 4 boxes also labeled 1 to 4, one card per box. What is the probability that no card gets placed into a box having the same label as the card?

$\mathrm{(A) \ } 1/3 \qquad \mathrm{(B) \ }3/8 \qquad \mathrm{(C) \ }5/12 \qquad \mathrm{(D) \ } 1/2 \qquad \mathrm{(E) \ }9/16$

Solution

The probability is $\frac{3!+2!+1!}{4!}=\frac{3}{8}$.

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