Question

Let A and B be two words sets containing 2 elements and 4 elements respectively. Find the number of subsets of $A\times B$ having 3 or more elements?

Answer 1

$A=\{x,y\}$

$B=\{a,b,c,d\}$

$A\times B$ having $2\times 4=8$ elements

Total subsets of $A\times B$ is $2^8=256$

$\therefore$ Total no. of subsets of $A\times B$ having $3$ or more elements

$=256-$ ($1$ nullset$+8$ singleton set$+8C2$ having $2$ elements)

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