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JEE Main20238 Apr 2023Morning ShiftMathematicsSets and RelationsActual

Let the number of elements in sets A and B be five and two respectively. Then the number of subsets of A × B each having at least 3 and at most 6 elements is

Options

  1. A752
  2. B782
  3. C792
  4. D772

Correct answer

C. 792

Step-by-step solution

Given, The number of elements in sets A and B be five and two respectively, So, n ( A ) = 5 and n ( B ) = 2 Now Cartesian product will be, n A × B = 10 Number of subsets having three elements = 10 C 3 Number of subsets having four elements = 10 C 4 Number of subsets having five elements = 10 C 5 Number of subsets having six elements = 10 C 6 So, number of subsets having atleast 3 and at most 6 elements will be = 10 C 3 + 10 C 4 + 10 C 5 + 10 C 6 = 120 + 210 + 252 + 210 = 792

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