If H = {1, 2, 3}, how many subsets of H have exactly 2 elements?

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Question: If H = {1, 2, 3}, how many subsets of H have exactly 2 elements?

Options:

Correct Answer: 6

Solution:

The number of ways to choose 2 elements from 3 is given by the combination formula C(3, 2) = 3.

If H = {1, 2, 3}, how many subsets of H have exactly 2 elements?

If H = {1, 2, 3}, how many subsets of H have exactly 2 elements?

Step 1: Identify the set H, which contains the elements {1, 2, 3}.
Step 2: Determine how many elements are in the set H. In this case, there are 3 elements.
Step 3: We want to find subsets of H that have exactly 2 elements.
Step 4: Use the combination formula C(n, k), where n is the total number of elements in the set and k is the number of elements we want to choose. Here, n = 3 and k = 2.
Step 5: Calculate C(3, 2) using the formula: C(n, k) = n! / (k! * (n - k)!).
Step 6: Substitute the values: C(3, 2) = 3! / (2! * (3 - 2)!) = 3! / (2! * 1!) = (3 * 2 * 1) / ((2 * 1) * (1)) = 3.
Step 7: Conclude that there are 3 subsets of H 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.