Question

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

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

Answer 1

The correct option is C $219$

$n\left(A\right)=2$, $n\left(S\right)=4$
$n(A\times B)=8$
Total number of subsets of $A\times B=2^8=256$
Total number of subsets of $A\times B$ having $3$ or more elements$=256-({}^8{C}_0+{}^8{C}_1+{}^8{C}_2)$
$=219$