Question

If $A$ and $B$ are 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

Answer 1

The correct option is A 219

Given, $n\left(A\right)=4,n\left(B\right)=2\Rightarrow n(A\times B)=8$
Total number of subsets of set $(A\times B)=2^8$
Number of subsets of set $A\times B$ having no element (i.e $\varphi )=1$
Number of subsets of set $A\times B$ having one element $={}^8{C}_1$
Number of subsets of set $A\times B$ having two elements $={}^8{C}_2\therefore$ Number of subsets having atleast three elements
$=2^8-(1+{}^8{C}_1+{}^8{C}_2)=2^8-1-8-28=256-37=219$