How many ways are there to choose 3 items from 6, without regard to order?

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Multiple Choice

How many ways are there to choose 3 items from 6, without regard to order?

Explanation:
Choosing 3 items from 6 without regard to order is a combinations problem. When order doesn’t matter, the number of ways to choose k items from n is C(n, k) = n! / (k!(n−k)!). Here that’s C(6,3) = 6! / (3!3!) = 720 / (6×6) = 20. You can also see this by counting sequences and then dividing by the 3! ways to arrange any chosen trio: (6×5×4) / (3×2×1) = 20. So there are 20 ways. If order mattered, it would be 6×5×4 = 120, which is not the scenario here.

Choosing 3 items from 6 without regard to order is a combinations problem. When order doesn’t matter, the number of ways to choose k items from n is C(n, k) = n! / (k!(n−k)!). Here that’s C(6,3) = 6! / (3!3!) = 720 / (6×6) = 20. You can also see this by counting sequences and then dividing by the 3! ways to arrange any chosen trio: (6×5×4) / (3×2×1) = 20. So there are 20 ways. If order mattered, it would be 6×5×4 = 120, which is not the scenario here.

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