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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?
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Q1
For the set E = {1, 2, 3, 4}, how many subsets have exactly 2 elements?
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The number of ways to choose 2 elements from 4 is given by the combination formula C(4,2) = 6.
Questions & Step-by-step Solutions
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Q
Q: For the set E = {1, 2, 3, 4}, how many subsets have exactly 2 elements?
Solution:
The number of ways to choose 2 elements from 4 is given by the combination formula C(4,2) = 6.
Steps: 9
Show Steps
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.
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