Roll four independent fair six-sided dice. Sort the four results and sum the three smallest values. What is the probability that this sum equals `3`? Derive the answer by characterizing the event and counting outcomes. Do not enumerate all `6^4` ordered rolls one by one. ### Constraints & Assumptions - Each die has faces `1` through `6` with equal probability. - Dice are distinguishable before sorting. - The three-smallest sum uses exactly three of the four results. ```hint Keep ordered and sorted outcomes distinct The dice are distinguishable when counting elementary outcomes even though the requested statistic uses their sorted values. ``` ### What a Strong Answer Covers - A precise translation from the sorted-value condition to a condition on ordered rolls. - An exhaustive favorable count with no overlaps or omissions. - A reduced probability and a sanity check. ### Follow-up Questions - What is the probability the three smallest sum to four? - How would the expression change for `n` dice and the `m` smallest? - What is the conditional distribution of the largest die under the event?