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
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 .
Solution 2
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
.
~abc2142
Video Solution
https://youtu.be/hwc11K02cEc - Happytwin
See Also
2007 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 23 |
Followed by Problem 25 | |
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