If a set has 4 elements, the number of subsets having at least 2 elements is?
- 10
- 11
- 12
- None of these
Explanation
For a set with n elements, total subsets = 2ⁿ
Here n = 4, so total subsets = 2⁴ = 16
"At least 2 elements" = total - subsets with 0 elements - subsets with 1 element
1. Subsets with 0 elements: C(4,0) = 1 → the empty set {}
2. Subsets with 1 element: C(4,1) = 4 → {a}, {b}, {c}, {d}
So subsets with ≥2 elements = 16 - 1 - 4 = 11
You can also do C(4,2) + C(4,3) + C(4,4) = 6 + 4 + 1 = 11
Last verified on 08-06-2026
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