1. The problem asks to find a trio (group of three digits) from the number 123456 without repeating any pair of digits. 2. We interpret "without repeating a pair" as selecting three digits such that no two digits form a pair that appears more than once in the trio. 3. Since the digits 1, 2, 3, 4, 5, 6 are all distinct, any trio of three different digits will have unique pairs. 4. The number of ways to choose 3 digits from 6 distinct digits is given by the combination formula: $$\binom{6}{3} = \frac{6!}{3!(6-3)!} = \frac{6 \times 5 \times 4}{3 \times 2 \times 1} = 20$$ 5. Each of these 20 trios contains unique pairs, so all are valid. 6. For example, one trio is (1, 2, 3). The pairs are (1,2), (1,3), and (2,3), all unique. Final answer: There are 20 possible trios from 123456 without repeating any pair.