Building a lunch box from three trays

Question

A food truck lets you build a lunch box by choosing exactly one item from each of three trays: 4 mains, 3 sides, and 5 drinks. How many different lunch boxes can you build?

Accepted Answer

This is the multiplication principle: when you make a series of independent choices, you multiply the number of options at each step. - Main: 4 ways. - Side: 3 ways. - Drink: 5 ways. Each main can be paired with each side, and each of those pairs with each drink, so nothing overlaps or repeats. The total is 4 	imes 3 	imes 5 = 60. A quick sanity check: fixing one specific main leaves 3 	imes 5 = 15 combinations, and there are 4 mains, giving 4 	imes 15 = 60 again. Takeaway. When independent choices are made one after another, multiply the counts. Adding a stage multiplies the total by tha…

Building a lunch box from three trays

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