Question

Let $A$ and $B$ be two sets containing four and two elements respectively.Then the number of subset of the set $A\times B$, each having at least three elements is

• A. $256$
• B. $275$
• C. $510$
• D. $219$

Answer 1

The correct option is D $219$

$A$ and $B$ containing $4$ and $2$ respectively

set A has 4 elements

set B has 2 elements

total number of element in $(A\times B)=4\times 2=8$

total number of subsets of $(A\times B)=2^8=256$

Number of subsets having 0 element $={{}^{8}C}_0=1$

Number of subsets having 1 element $={{}^{8}C}_1=8$

number of subsets having 2 element $={{}^{8}C}_2=\frac{8\times 7}{2}=28$

Number of subsets having atleast 3 elements

$=256-28-8-1=219$