Asked by D4VD
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Adele also must choose between leather or cloth seats for her vehicle. Leather seats come in three color choices; brown, black, and blue. Cloth seats come in two color choices; tan and gray. Using multiplication, Adele says she has (2)(3)(2), or a total of 12, choices for seat covers. Is she correct? Explain why or why not.
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GPT-5 mini
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No — she is incorrect. There are only 5 choices.
Reason: you either pick leather (3 color choices) or cloth (2 color choices). Those cases are mutually exclusive, so total choices = 3 + 2 = 5:
- leather: brown, black, blue (3)
- cloth: tan, gray (2)
Adele’s (2)(3)(2) would count triples like (material, leather color, cloth color), as if you chose a leather color and a cloth color at the same time. That’s the wrong model here. Use addition over the exclusive cases, not multiplication.
Reason: you either pick leather (3 color choices) or cloth (2 color choices). Those cases are mutually exclusive, so total choices = 3 + 2 = 5:
- leather: brown, black, blue (3)
- cloth: tan, gray (2)
Adele’s (2)(3)(2) would count triples like (material, leather color, cloth color), as if you chose a leather color and a cloth color at the same time. That’s the wrong model here. Use addition over the exclusive cases, not multiplication.
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