Difference between revisions of "2007 AMC 8 Problems/Problem 24"
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| − | + | ==Problem== | |
| + | A bag contains four pieces of paper, each labeled with one of the digits <math>1</math>, <math>2</math>, <math>3</math> or <math>4</math>, with no repeats. Three of these pieces are drawn, one at a time without replacement, to construct a three-digit number. What is the probability that the three-digit number is a multiple of <math>3</math>? | ||
| + | <math> \textbf{(A)}\ \frac{1}{4}\qquad\textbf{(B)}\ \frac{1}{3}\qquad\textbf{(C)}\ \frac{1}{2}\qquad\textbf{(D)}\ \frac{2}{3}\qquad\textbf{(E)}\ \frac{3}{4} </math> | ||
| − | + | ==Solution== | |
| + | The combination of digits that give multiples of 3 are (1,2,3) and (2,3,4). The number of ways to choose three digits out of four is 4. Therefore, the probability is <math>\textbf{(C)}\ \frac{1}{2}</math>. | ||
Revision as of 22:49, 9 December 2012
Problem
A bag contains four pieces of paper, each labeled with one of the digits 
, 
, 
or 
, with no repeats. Three of these pieces are drawn, one at a time without replacement, to construct a three-digit number. What is the probability that the three-digit number is a multiple of ?
Solution
The combination of digits that give multiples of 3 are (1,2,3) and (2,3,4). The number of ways to choose three digits out of four is 4. Therefore, the probability is 
.
