If A has 5 elements, how many subsets of A will contain one fixed element?
Answer and explanation
Correct answer: 16
Let one particular element be fixed and required to appear in every selected subset. That element has no choice because it must be included. Each of the remaining four elements can independently be included or excluded, giving two choices for each. Therefore the number of subsets is 2^4 = 16. This is half of the total 2^5 subsets, since exactly half contain the chosen element.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
Let one particular element be fixed and required to appear in every selected subset. That element has no choice because it must be included. Each of the remaining four elements can independently be included or excluded, giving two choices for each. Therefore the number of subsets is 2^4 = 16. This is half of the total 2^5 subsets, since exactly half contain the chosen element.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
