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Combination with Restrictions

Let A and B b...

Question

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

A

256

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B

220

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C

219

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D

211

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Solution

The correct option is C 219
$A = x, y B = a, b, c, d A \times B h a v i n g 2 \times 4 = 8 e l e m e n t s T o t a l s u b s e t s A \times B = 2^{8} = 256 ∴ T o t a l n o . o f s u b s e t s o f A \times B h a v i n g 3 o r m o r e e l e m e n t s = 256 - ⎛ ⎜ ⎝ \begin{matrix} 18^{8} C_{2} n u l l + s i n g l e t o n + s u b s e t h a v i n g s e t s e t 2 e l e m i n t s \end{matrix} ⎞ ⎟ ⎠ = 256 - 1 - 8 - 28 = 219$

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