If A = {a,b,c,d,e,f,g}, how many 4-element subsets of P(A) contain a and do not contain b?
Answer and explanation
Correct answer: 10
We are counting 4-element subsets of A, not subsets of the power set as objects of a second-level selection. The element a must be included and b must be excluded. Thus, one of the four positions is already occupied by a, while the remaining three elements must be chosen from c,d,e,f,g, which gives five available elements. The number of choices is C(5,3) = 5!/(3!2!) = 10. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
10
Why is this the correct answer?
We are counting 4-element subsets of A, not subsets of the power set as objects of a second-level selection. The element a must be included and b must be excluded. Thus, one of the four positions is already occupied by a, while the remaining three elements must be chosen from c,d,e,f,g, which gives five available elements. The number of choices is C(5,3) = 5!/(3!2!) = 10. Hence option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
