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

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

Options:

  1. 4
  2. 6
  3. 8
  4. 10

Correct Answer: 6

Solution: 

The number of ways to choose 2 elements from 4 is given by the combination formula C(4,2) = 6.

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

Practice Questions

Q1
For the set E = {1, 2, 3, 4}, how many subsets have exactly 2 elements?
  1. 4
  2. 6
  3. 8
  4. 10

Questions & Step-by-Step Solutions

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.
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