Alex is embarking on a new meal plan that allows him to select either a smoothie or oatmeal for breakfast, 5 different options for lunch, and 8 different options for dinner. If Alex opts for a Mexican dish for lunch, he will always select a Mexican dish for dinner. Conversely, if he chooses a Thai dish for lunch, he will not choose a Thai dish for dinner. Given that there are 3 Mexican dishes and 2 Thai dishes available for lunch, and 4 Mexican dishes and 2 Thai dishes available for dinner, how many unique daily meal combinations can Alex create?

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Alex is embarking on a new meal plan that allows him to select either a smoothie or oatmeal for breakfast, 5 different options for lunch, and 8 different options for dinner. If Alex opts for a Mexican dish for lunch, he will always select a Mexican dish for dinner. Conversely, if he chooses a Thai dish for lunch, he will not choose a Thai dish for dinner. Given that there are 3 Mexican dishes and 2 Thai dishes available for lunch, and 4 Mexican dishes and 2 Thai dishes available for dinner, how many…

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What this question tests

What it tests

Whether you can count arrangements and selections correctly — permutations vs. combinations.

Common trap

Overcounting: treating a selection as ordered when order does not matter, or forgetting to divide by duplicates.