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Question

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:
(IIT JEE Main 2015)

A
219
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B
256
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C
275
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D
510
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Solution

The correct option is A 219
Number of elements in Set A = 4
Number of elements in Set B = 2
Number of elements in set (A × B) = 4 × 2 = 8
Total number of subsets of (A × B) = 28=256
Number of subsets having 0 elements = 8C0=1
Number of subsets having 1 element each = 8C1=8
Number of subsets having 2 elements each = 8C2=28
Number of subsets having at least 3 elements = 256-1-8-28 = 219

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