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

Solution :

Given, n(A) = 2 and n(B) = 4

\(\therefore\) n(A\(\times\)B) = 8

The number of subsets of (A\(times\)B) having 3 or more elements = \(^8C_3 + {^8C_4} + ….. + {^8C_8}\)

= \(2^8 – {^8C_0} – {^8C_1} – {^8C_2}\)

= 256 – 1 – 8 – 28 = 219     [\(\because\) \(2^n\) = \(^nC_0  + {^nC_1} + ….. + {^nC_n}\)]


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