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Question: A robotics engineer is programming a surgical robot that selects one of 4 tools at random for each of 5 procedures, with equal probability. What is the probability that the robot uses each tool at least once over the 5 procedures?
We count the number of sequences of length 5 using 4 tools where each tool appears at least once. This is given by the inclusion-exclusion principle:
If a car travels 150 miles in 3 hours, what is its average speed in miles per hour, and how far will it travel in 7 hours at that speed?

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