If A = {1,2,3,4,5,6}, how many 4-element subsets of A contain both 1 and 2?
Answer and explanation
Correct answer: 6
The elements 1 and 2 are required, so they occupy two of the four positions. We must choose the remaining two elements from {3,4,5,6}, which has four elements. Using combinations, the count is C(4,2) = 4!/(2!2!) = 6. Thus option B is correct. Choosing C(4,1), C(5,2), or C(6,2) would not enforce both required elements correctly.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
The elements 1 and 2 are required, so they occupy two of the four positions. We must choose the remaining two elements from {3,4,5,6}, which has four elements. Using combinations, the count is C(4,2) = 4!/(2!2!) = 6. Thus option B is correct. Choosing C(4,1), C(5,2), or C(6,2) would not enforce both required elements correctly.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
