A)
B) 275
C) 510
D) 219
E) 256
Correct Answer: D
Solution :
\[n\left( A \right)=4\]and\[n\left( B \right)=2\] \[\Rightarrow \]\[\eta (A\times B)=8\] Hence number of subsets of \[(A\times B)\]each having at least three elements is equal to \[^{8}{{C}_{3}}{{+}^{8}}{{C}_{4}}{{+}^{8}}{{C}_{5}}+.....{{+}^{8}}{{C}_{8}}\] \[={{2}^{8}}{{-}^{8}}{{C}_{0}}{{+}^{8}}{{C}_{1}}{{-}^{8}}{{C}_{2}}\] \[=256-1-8-28=219\]
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