3-Digit Duel

What this combinatorial probability question tests

This is a medium-difficulty probability problem that combines counting, sampling without replacement, and direct comparison. It rewards clear enumeration of outcomes and careful handling of the constraint that ties favour Player A.

To solve it, you must count the total number of distinct three-digit numbers each player can form, then determine in how many of those comparisons Player B's number is strictly larger. The key insight is that once digits are fixed, their ordering into a number is deterministic, so the randomness lies entirely in the selection of which numbers each player draws.

• Combinations and permutations with constraints
• Counting outcomes in a finite sample space
• Joint probability over independent selections
• Strict inequality and tie-breaking rules