If a set A has 5 elements, how many three-element subsets does A have?
Answer and explanation
Correct answer: 10
A three-element subset is formed by choosing 3 different elements from the 5 elements of A, and the order of selection does not matter. Therefore, the required number is the combination 5C3 = 5!/(3!2!) = (5×4)/(2×1) = 10. Choosing the same three elements in another order does not create a new subset, which is why combinations rather than permutations are used.
Frequently asked questions
What is the correct answer to this question?
10
Why is this the correct answer?
A three-element subset is formed by choosing 3 different elements from the 5 elements of A, and the order of selection does not matter. Therefore, the required number is the combination 5C3 = 5!/(3!2!) = (5×4)/(2×1) = 10. Choosing the same three elements in another order does not create a new subset, which is why combinations rather than permutations are used.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
