How many 3-element subsets can be formed from a 6-element set?

How many 3-element subsets can be formed from a 6-element set?

• A. 30
• B. 20
• C. 10
• D. 15

Answer: (B)

Counting how many 3-element subsets can be formed from 6 elements means choosing 3 elements where order doesn’t matter. This is a combination: 6 choose 3. Compute it as 6×5×4 divided by 3×2×1, which equals 20. Intuitively, you could count all ordered triples (6×5×4) and then divide by 3! to ignore the order of the three elements, leaving 20 distinct subsets. So there are 20 such subsets.

Counting how many 3-element subsets can be formed from 6 elements means choosing 3 elements where order doesn’t matter. This is a combination: 6 choose 3. Compute it as 6×5×4 divided by 3×2×1, which equals 20. Intuitively, you could count all ordered triples (6×5×4) and then divide by 3! to ignore the order of the three elements, leaving 20 distinct subsets. So there are 20 such subsets.