This math topic focuses on calculating the number of distinct ways to order 3 cards, some of which may be identical (i.e., repeats). These problems utilize permutations and factorial operations to determine the total arrangements possible given the repetition of certain cards. Students are asked to express their answers in a factorial form, enhancing their understanding of probability, statistics, and factorial calculations. The questions provide various answer options, represented in LaTeX expressions, requiring students to evaluate and choose the correct factorial expressions corresponding to each scenario.
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How many distinct ways can these cards be ordered? Show as a factorial.