Question

Let $A$ and $B$ be two sets containing $2$ 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 $219$

$n\left(A\right)=2$ and $n\left(B\right)=4$

$n(A\times B)=8$

Number of subslts of $A\times B$ having $3$ or more elements.

${=}^8{C}_3{+}^8{C}_4{+}^8{C}_5{+}^8{C}_6{+}^8{C}_7{+}^8{C}_8$

$=219$