If A = {a, b, c, d, e, f, g}, how many subsets of A contain exactly 6 elements?
Answer and explanation
Correct answer: 7
A has 7 elements, and a subset containing exactly 6 elements can be formed by choosing 6 of them. Therefore, the number is C(7,6) = 7. An even simpler view is that each such subset is obtained by omitting exactly one element from A, and there are 7 possible elements to omit. Hence option B is correct. The value 21 is C(7,2), not C(7,6).
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
A has 7 elements, and a subset containing exactly 6 elements can be formed by choosing 6 of them. Therefore, the number is C(7,6) = 7. An even simpler view is that each such subset is obtained by omitting exactly one element from A, and there are 7 possible elements to omit. Hence option B is correct. The value 21 is C(7,2), not C(7,6).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
