2007 AMC 8 Problems/Problem 24
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 1
The number of ways to form a 3-digit number is . The combination of digits that give us multiples of 3 are (1,2,3) and (2,3,4), as the integers in the subsets have a sum which is divisible by 3. The number of 3-digit numbers that contain these numbers is . Therefore, the probability is .
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Solution 2
Only (1,2,3) and (2,3,4) are possible combinations that sum to 3. The total ways to choose three numbers from the four numbers is 4 choose 3 which equals 4. The answer is .
Video Solution
https://youtu.be/hwc11K02cEc - Happytwin
Video Solution 2
https://youtu.be/cUxFS9l-Pb4 - Soo, DRMS, NM
See Also
2007 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 23 |
Followed by Problem 25 | |
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All AJHSME/AMC 8 Problems and Solutions |
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