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EEJ MAIN Mathematics QUESTION #7439
Question 1
Let A and B be two sets containing four and two elements respectively. Then the number of subsets of the set A × B, each having at least three elements, is:
  • 219✔️
  • 256
  • 275
  • 510
Correct Answer Explanation
The set \(A \times B\) has \(4 \times 2 = 8\) elements. Total number of subsets is \(2^8 = 256\). Subsets with 0 elements: \(\binom{8}{0} = 1\). Subsets with 1 element: \(\binom{8}{1} = 8\). Subsets with 2 elements: \(\binom{8}{2} = 28\). Subsets with at least 3 elements = \(256 - 1 - 8 - 28 = 219\).