Sum to 5

What this subset-sum probability question tests

This is a medium-difficulty probability question that combines enumeration with logical reasoning about sets. It asks you to find the probability of a specific structural property across all possible dice outcomes, requiring careful accounting of which face combinations satisfy the constraint.

The core challenge is understanding what "any subset can sum to 5" means in practice: you must check all possible subsets of the three dice and verify that at least one of them totals to exactly 5. This demands systematic case analysis and clear notation to avoid double-counting or missing configurations.

• Sample space and outcome enumeration for multiple dice
• Subset properties and logical conditions
• Complementary counting and inclusion-exclusion