2009 AMC 8 Problems/Problem 13
Problem
A three-digit integer contains one of each of the digits , , and . What is the probability that the integer is divisible by ?
Solution
The three digit numbers are . The numbers that end in are divisible are , and the probability of choosing those numbers is .
Alternate Solution
The number is odd if and only if the number ends in (also , but that case can be ignored, as none of the digits are ) If we randomly arrange the three digits, the probability of the last digit being is .
Note: The last sentence is true because there are randomly-arrangeable numbers)
See Also
2009 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 12 |
Followed by Problem 14 | |
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