How many ways are there to choose 3 objects from 5 distinct objects without repetition?

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Multiple Choice

How many ways are there to choose 3 objects from 5 distinct objects without repetition?

Explanation:
Choosing 3 objects from 5 distinct items without repetition is about counting unordered selections. Since the order doesn’t matter, you use combinations: the number of ways is 5 choose 3, which equals 5!/(3!2!) = 120/(6×2) = 10. By symmetry, 5 choose 3 equals 5 choose 2, which is also 10. If order mattered, the count would be 5P3 = 5×4×3 = 60, but that’s not the scenario here. So there are 10 ways.

Choosing 3 objects from 5 distinct items without repetition is about counting unordered selections. Since the order doesn’t matter, you use combinations: the number of ways is 5 choose 3, which equals 5!/(3!2!) = 120/(6×2) = 10. By symmetry, 5 choose 3 equals 5 choose 2, which is also 10. If order mattered, the count would be 5P3 = 5×4×3 = 60, but that’s not the scenario here. So there are 10 ways.

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