2007 AMC 8 Problems/Problem 24

Problem

A bag contains four pieces of paper, each labeled with one of the digits $1$ , $2$ , $3$ or $4$ , 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 $3$ ? $\textbf{(A)}\ \frac{1}{4}\qquad\textbf{(B)}\ \frac{1}{3}\qquad\textbf{(C)}\ \frac{1}{2}\qquad\textbf{(D)}\ \frac{2}{3}\qquad\textbf{(E)}\ \frac{3}{4}$

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 $\textbf{(C)}\ \frac{1}{2}$ .

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2007 AMC 8 Problems/Problem 24

Problem

Solution