Let A and B be two sets containing four and two elements respectively. Then, the number of subsets of the set $A \times B$, each having atleast three elements are
(A)
219
(B)
256
(C)
275
(D)
510
MEDIUM
Correct Answer:A
Explanation
Given, $n(A) = 4$, $n(B) = 2$
$\Rightarrow n(A \times B) = 8$
Total number of subsets of set $(A \times B) = 2^8$
Number of subsets of set $A \times B$ having no element (i.e. $\phi$) = $1$
Number of subsets of set $A \times B$ having one element = $^8C_1$
Number of subsets of set $A \times B$ having two elements = $^8C_2$
$\therefore$ Number of subsets having atleast three elements = $2^8 - (1 + ^8C_1 + ^8C_2)$ = $2^8 - 1 - 8 - 28$ = $2^8 - 37$ = $256 - 37 = 219$