Problem:
A three-digit integer contains one of each of the digits and . What is the probability that the integer is divisible by
Answer Choices:
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E.
Solution:
There are three-digit numbers possible using the digits and once each: and . Because the numbers divisible by end in or , only and are divisible by . The probability that the three-digit number is divisible by is .
The number is equally likely to end in or . The number is divisible by only if it ends in , so the probability is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions