Counting subsets — Aptitude Question
Counting subsets: How many subsets does a set of 6 elements have, including the empty set? Answer and worked solution on CodeKairo.
- Topic: Permutations & Combinations
- Section: Quantitative Aptitude
- Difficulty: Easy
- Time target: 45 seconds
Question
How many subsets does a set of 6 elements have, including the empty set?
Options
- 12
- 32
- 64
- 720
Show the answer and the worked solution
Correct answer: C. 64
Worked solution
- Each of the 6 elements may be included or excluded: 2⁶ = 64.
Answer: 64.
The idea
Total subsets are 2ⁿ; non-empty subsets are 2ⁿ − 1. Which the question wants is worth checking twice.
Shortcut. The subset counts by size are row 6 of Pascal's triangle: 1 + 6 + 15 + 20 + 15 + 6 + 1 = 64 = 2⁶.
Common trap. "12" — multiplying 2 × 6 instead of raising 2 to the sixth power.
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