CMA Foundation · Fundamentals of Business Mathematics and Statistics · Set Theory, including Venn Diagram
A set P has 6 elements. How many of its subsets contain exactly 2 elements, and how many proper subsets does P have in all?
There are 6C2 = 15 subsets with exactly two elements. The total number of subsets is 2⁶ = 64, and removing the set itself leaves 63 proper subsets. So the correct pair is 15 and 63.
- A15 and 63Correct
- B12 and 64
- C15 and 64
- D30 and 63
Explanation
Subsets with exactly 2 elements number 6C2 = 6×5/2 = 15. Total subsets are 2⁶ = 64, and proper subsets exclude P itself, giving 63. Option 64 forgets to exclude the set itself, and 30 uses 6P2 (ordered selection).
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