If A = {a, b, c, d, e}, how many subsets contain a, do not contain c, and have exactly 3 elements?
Answer and explanation
Correct answer: 3
The element a must be included, while c must be excluded. Therefore, one position is already fixed and c cannot be selected. To make a 3-element subset, we need two more elements from the remaining available elements b, d, and e. The number of ways is C(3,2) = 3. The subsets are {a,b,d}, {a,b,e}, and {a,d,e}. Hence option B is correct.
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
The element a must be included, while c must be excluded. Therefore, one position is already fixed and c cannot be selected. To make a 3-element subset, we need two more elements from the remaining available elements b, d, and e. The number of ways is C(3,2) = 3. The subsets are {a,b,d}, {a,b,e}, and {a,d,e}. Hence 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.
