If A = {1,2,3,4,5,6,7}, how many subsets in P(A) have at least 6 elements?
Advertisement
Answer and explanation
Correct answer: 8
“At least 6 elements” includes subsets having exactly 6 elements and exactly 7 elements. From a 7-element set, the number of 6-element subsets is C(7,6) = 7, because one element is omitted. The number of 7-element subsets is C(7,7) = 1, namely A itself. Therefore the total is 7 + 1 = 8, so option B is correct.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
“At least 6 elements” includes subsets having exactly 6 elements and exactly 7 elements. From a 7-element set, the number of 6-element subsets is C(7,6) = 7, because one element is omitted. The number of 7-element subsets is C(7,7) = 1, namely A itself. Therefore the total is 7 + 1 = 8, so option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
Advertisement