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Let A and B be two sets containing 2 ele...

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

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The correct Answer is:
219
Given, `n(A) = 2,n(B) = 4`
`therefore n(A xx B) = 8`
The number of subsets of `A xx B` having 3 or more elements
`= ""^(8)C_(3) + ""^(8)C_(4)+.......+""^(8)C_(8)`
`= (""^(8)C_0 + ""^(8)C_1 +""^(8)C_2 +""^(8)C_3 ........ +""^(8)C_8)`
` - (""^(8)C_(0) + ""^(8)C_1 + ""^(8)C_(2))`
`therefore = 2^(8)-""^(8)C_(0)-""^(8)C_(1)-""^(8)C_(2)`
`= 256 -1 -8-28 = 219`
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