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NDA 2025 Maths · Mathematics · Sets, Relations and Functions · easy

The number of subsets of the set A=\1,2,3,4,5\ having at least 3 elements is

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The number of subsets of the set A={1,2,3,4,5}A=\{1,2,3,4,5\} having at least 3 elements is
  1. A. 1616
  2. B. 2626
  3. C. 1010
  4. D. 3232
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Answer: (A) 1616

Subsets with 3, 4 and 5 elements number (53)+(54)+(55)=10+5+1=16\binom53+\binom54+\binom55=10+5+1=16. The trap is 2626, which comes from subtracting only the subsets with 0 and 1 element from 3232 and forgetting the (52)=10\binom52=10 subsets with exactly 2 elements.
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Original question written in the NDA 2025 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake