For the set E = {1, 2, 3, 4}, how many subsets have exactly 2 elements?

For the set E = {1, 2, 3, 4}, how many subsets have exactly 2 elements?

Correct Answer: 6

Step 1: Understand what a subset is. A subset is a group of elements taken from a larger set.
Step 2: Identify the set E, which is {1, 2, 3, 4}.
Step 3: Determine how many elements are in the set E. There are 4 elements.
Step 4: We want to find subsets that have exactly 2 elements.
Step 5: Use the combination formula C(n, k) to find the number of ways to choose k elements from n elements. Here, n = 4 and k = 2.
Step 6: The combination formula is C(n, k) = n! / (k! * (n - k)!).
Step 7: Calculate C(4, 2): C(4, 2) = 4! / (2! * (4 - 2)!) = 4! / (2! * 2!)
Step 8: Calculate the factorials: 4! = 24, 2! = 2, so C(4, 2) = 24 / (2 * 2) = 24 / 4 = 6.
Step 9: Conclude that there are 6 subsets of E that have exactly 2 elements.

Combinations – The concept of combinations is used to determine the number of ways to choose a subset of items from a larger set without regard to the order of selection.