Customizing a phone case in three steps

Question

An online shop lets you design a phone case by picking one option from each category: 6 colors, 4 patterns, and 2 finishes (matte or glossy). How many different phone cases can be designed?

Accepted Answer

Each design is an independent choice from three categories, so we multiply the number of options at each stage (the multiplication principle): 6 	imes 4 	imes 2 = 48. To see there is no double counting, note that two designs are the same only if they match on color, pattern, and finish all at once. Since each stage is chosen separately, every combination is distinct. Takeaway. Independent design choices multiply. Here three categories give 6 	imes 4 	imes 2 = 48 possibilities.

Customizing a phone case in three steps

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