If A and B are two sets containing 2 elements and 4 elements, respectively. Then, the number of subsets of `A xx B` having 3 or more elements, is

Options

A. 256
B. 220
C. 219
D. 211

Explanation

we have , `n(A) = 2 and n(B)=4`
`therefore n(AxxB)=n(A) xxn(B) = 2xx4=8`
the number of subsets of A`xx` B having 3 or more elements
`""^(8)C_(3)+""^(8)C_(4)+""^(8)C_(5)+""^(8)C_(7)+""^(8)C_(8)`
`=(""^(8)C_(0) +""^(8) C_(1)+. . . . . . . . . . . +""^(8)C_(8))-(""^(8) C_(0) +""^(8)C_(1)+""^(8)C_(2))`
`=2^(8)-(1+8+28)=219`