If \(A=\{w,x,y,z\}\), how many three-element subsets does \(A\) have?
Answer and explanation
Correct answer: 4
A three-element subset is formed by choosing 3 of the 4 elements \(w,x,y,z\), without regard to order. Therefore, the number is \(\binom{4}{3}=\frac{4!}{3!1!}=4\). The four subsets are \(\{w,x,y\}\), \(\{w,x,z\}\), \(\{w,y,z\}\), and \(\{x,y,z\}\). Option B, 6, counts two-element subsets using \(\binom{4}{2}\), while option D is not the required combination count.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
A three-element subset is formed by choosing 3 of the 4 elements \(w,x,y,z\), without regard to order. Therefore, the number is \(\binom{4}{3}=\frac{4!}{3!1!}=4\). The four subsets are \(\{w,x,y\}\), \(\{w,x,z\}\), \(\{w,y,z\}\), and \(\{x,y,z\}\). Option B, 6, counts two-element subsets using \(\binom{4}{2}\), while option D is not the required combination count.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
