Q121 / 240 · KCET 2026 · Mathematics
If $A = \{a, b, c, d, e, f\}$, then the number of subsets of A which contains at least $2$ elements is
- A$64$
- B$65$
- Correct answerC$57$
- D$59$
Solution
Total number of elements in set $A$ is $n = 6$.
Total number of subsets of $A$ is $2^6 = 64$.
Number of subsets containing $0$ elements is $^{6}C_{0} = 1$.
Number of subsets containing $1$ element is $^{6}C_{1} = 6$.
Number of subsets containing at least $2$ elements is equal to the total number of subsets minus the number of subsets with $0$ or $1$ element.
Required number of subsets $= 64 - (1 + 6) = 57$.
Answer: $57$
Total number of subsets of $A$ is $2^6 = 64$.
Number of subsets containing $0$ elements is $^{6}C_{0} = 1$.
Number of subsets containing $1$ element is $^{6}C_{1} = 6$.
Number of subsets containing at least $2$ elements is equal to the total number of subsets minus the number of subsets with $0$ or $1$ element.
Required number of subsets $= 64 - (1 + 6) = 57$.
Answer: $57$
Hence, the correct answer is option: 'C'.