Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of A × B having 3 or more elements is :

Engineering

Mathematics

Sets

Question

211

219

220

256

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A $\to_{}^{}$ 2 elements

B $\to_{}^{}$ 4 elements

n(A × B) = 2 × 4 = 8

$∴$ number of subset having 3 or more element

= ⁸C₈ + ⁸C₇ + ⁸C₆ + ⁸C₅ + ⁸C₄ + ⁸C₃

= 28 – (⁸C₂ + ⁸C₁ + ⁸C₀)

= 256 – [28 + 8 + 1]

= 219 Ans.