# Killer monkeys

**Discrete Mathematics**Level 5

On a ladder of 21 steps, numbered \(\{-10,-9,-8,\cdots,8,9,10\},\) a monkey named Harry sits on step 0 and another monkey named Berry sits on step 2. Now, each monkey makes 10 moves simultaneously, and those 10 moves consist of 6 moves up and 4 moves down the ladder for both. During this procedure, the monkeys slap each other every time they happen to be on the same step. The probability that the monkeys are slapped at least once during this process can be expressed as \(\frac{a}{b}\) where \(a\) and \(b\) are coprime integers. Find \(a+b.\)

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