This math topic revolves around calculating the different ways to order a set of five cards, some of which may be repeated, using factorial notation. It falls under the broader category of probability and statistics focusing specifically on factorials to determine permutations of items where order matters. The questions require the students to analyze a given situation, invoking their knowledge of factorials to provide solutions in the form of distinct ordering possibilities. The equations involved typically consist of factorials divided by the product of factorials, reflecting the constraints posed by identical items (repeats) among the cards.
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How many distinct ways can these cards be ordered? Show as a factorial.