If A has 6 elements, how many elements of P(A) do not have exactly 2 elements?
Answer and explanation
Correct answer: 49
A set with 6 elements has 2^6=64 total subsets. The subsets containing exactly 2 elements are counted by choosing 2 elements from 6: C(6,2)=6×5/2=15. The required subsets are all subsets except these 15, so their number is 64−15=49. This includes subsets of sizes 0, 1, 3, 4, 5, and 6; the empty set is also an element of the power set.
Frequently asked questions
What is the correct answer to this question?
49
Why is this the correct answer?
A set with 6 elements has 2^6=64 total subsets. The subsets containing exactly 2 elements are counted by choosing 2 elements from 6: C(6,2)=6×5/2=15. The required subsets are all subsets except these 15, so their number is 64−15=49. This includes subsets of sizes 0, 1, 3, 4, 5, and 6; the empty set is also an element of the power set.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
