If A and B are two sets containing four and two elements, respectively. Then, the number of subsets of the set A×B each having atleast three elements are
A
219
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B
510
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C
275
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D
256
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Solution
The correct option is A 219 Given, n(A)=4,n(B)=2⇒n(A×B)=8
Total number of subsets of set (A×B)=28
Number of subsets of set A×B having no element (i.e ϕ)=1
Number of subsets of set A×B having one element =8C1
Number of subsets of set A×B having two elements =8C2∴ Number of subsets having atleast three elements =28−(1+8C1+8C2)=28−1−8−28=256−37=219