If you have 10 tops, 5 bottoms, and 3 pairs of shoes, how many outfits can you form by choosing one item from each category (order within an outfit does not matter)?

If you have 10 tops, 5 bottoms, and 3 pairs of shoes, how many outfits can you form by choosing one item from each category (order within an outfit does not matter)?

• A. 150
• B. 75
• C. 30
• D. 450

Answer: (A)

The key idea is counting with independent choices using multiplication. An outfit is formed by picking one item from each category, and the choice in one category doesn’t affect how many choices you have in the other categories. You start with the top options: 10 different tops. For each top, you can pair it with any of 5 bottoms, giving 10 × 5 = 50 top-bottom combinations. For every one of those combinations, you can choose among 3 pairs of shoes, so you multiply again: 50 × 3 = 150 total outfits. Since an outfit is defined by the specific items worn, not the order you pick them, there’s no need to count different sequences separately. The product 10 × 5 × 3 already counts each distinct trio of items exactly once. If someone were to ignore a category or treat the order of selection as meaningful, they’d get a different (incorrect) total. Here, the straightforward product gives 150 outfits.

The key idea is counting with independent choices using multiplication. An outfit is formed by picking one item from each category, and the choice in one category doesn’t affect how many choices you have in the other categories.

You start with the top options: 10 different tops. For each top, you can pair it with any of 5 bottoms, giving 10 × 5 = 50 top-bottom combinations. For every one of those combinations, you can choose among 3 pairs of shoes, so you multiply again: 50 × 3 = 150 total outfits.

Since an outfit is defined by the specific items worn, not the order you pick them, there’s no need to count different sequences separately. The product 10 × 5 × 3 already counts each distinct trio of items exactly once.

If someone were to ignore a category or treat the order of selection as meaningful, they’d get a different (incorrect) total. Here, the straightforward product gives 150 outfits.