Question

Let $A$ and $B$ be two sets containing 4 and 2 elements respectively. Then the number of subsets of the set $A\times B$, each having at least three elements is

• A. $219$
• B. $235$
• C. $228$
• D. $256$

Answer 1

The correct option is A $219$

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

$\therefore n(A\times B)=8$

Thus the number of subsets of $A\times B$ having at least 3 elements

$=2^8{-}^8{C}_0{-}^8{C}_1{-}^8{C}_2=256-1-8-28=219$