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๐ฐ Question: A science communicator films a video in segments, each segment using one of 4 different visual effects: animation, simulation, data overlay, or live-action. If the 8-segment video must contain exactly 3 animations, 2 simulations, 2 data overlays, and 1 live-action segment, how many distinct editing orders are possible?
๐ฐ Solution: We are arranging a sequence of 8 video segments with fixed counts: 3 animations (A), 2 simulations (S), 2 data overlays (D), and 1 live-action (L). Since the segments of the same type are indistinct in effect (though filmed separately), we are counting the number of distinct permutations of a multiset. The number of distinct editing orders is:
๐ฐ Thus, the number of distinct editing orders is:
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