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Step 2: For each such pair, how many ways can the three integers be assigned to $a$ and $b$ such that both appear at least once?
The total assignments: $2^3 = 8$, but subtract the 2 cases where all are $a$ or all are $b$. So $8 - 2 = 6$ valid binary strings with both values present.
Thus, number of favorable outcomes:

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