Numbers with equal mean and median

Discrete Mathematics Level 3

Three distinct positive integers less than or equal to 15 are chosen. The probability that the mean of these numbers is equal to the median can be expressed as \(\frac{a}{b}\) where \(a\) and \(b\) are coprime positive integers. What is the value of \(a + b\)?

Details and assumptions

The mean of a set of numbers is the average of the set.
The median of a set of numbers is the middle value, which divides the list into two equal halves. If there is an even number of them, the median will be the mean of the two middle values.


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