If A = {1,2,3,4,5,6}, how many 3-element subsets in P(A) contain 1 and do not contain 6?
Advertisement
Answer and explanation
Correct answer: 6
The required subset must contain 1, so that element is already fixed. It must not contain 6, so 6 is excluded. To make a 3-element subset, two more elements must be selected from the remaining allowed set {2,3,4,5}. The number of choices is C(4,2) = 6. Therefore, option B is the correct answer.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
The required subset must contain 1, so that element is already fixed. It must not contain 6, so 6 is excluded. To make a 3-element subset, two more elements must be selected from the remaining allowed set {2,3,4,5}. The number of choices is C(4,2) = 6. Therefore, option B is the correct answer.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
Advertisement