Choosing Integers

Number Theory Level pending

There are 15 (not necessarily distinct) integers chosen uniformly at random from the range from 0 to 999, inclusive. Albert then computes the sum of their units digits, while Bob computes the last three digits of their sum. The probability of them getting the same result is \(\frac mn\), for relatively prime positive integers \(m\) and \(n\). Find \(10m+n\).

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