Each named tile is a physical object. Keeping the first tile out removes that same object from the second choices. Exclude same-name pairs, but keep both orders of different tiles. At least one star includes one or two stars; exactly one excludes two stars. These events can have equal chances when two stars are impossible. Reset the bag for each question.
Worked example
A worked bag has S1, C1 and C2. Keep the first tile out. There are 3 x 2 = 6 allowed paths. Four have exactly one star; two have zero stars. There is only one physical star, so no allowed pair has two stars. At least one and exactly one both have chance 4/6 here. They are not always equal.