A star first OR a star second includes both. Add the first-star and second-star counts, then subtract their two-star overlap once. Keep the same sample space for every count. With no returns, exclude same-physical-tile pairs before counting. If an overlap is empty, adding the two counts is enough. Reset the stated bag for each question.
Worked example
A worked bag has S1, S2, C1 and C2. Keep the first tile out. Among twelve allowed paths, six start with a star and six end with a star. Two paths have stars in both positions. At least one star therefore has 6 + 6 - 2 = 10 paths, or 10/12. Adding six and six alone would count the overlap twice.