Solution: The problem requires distributing 5 distinct keys to 3 distinct servers with each server receiving at least one key. This is a classic inclusion-exclusion problem. The total number of ways to assign the keys without restriction is $3^5$. Subtract the cases where at least one server gets no keys: $\binom31 \cdot 2^5$. Add back the cases where two servers get no keys (since they were subtracted twice): $\binom32 \cdot 1^5$. Thus, the total is: - Abu Waleed Tea
Mar 01, 2026
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