Question

Let $A\&B$ be two sets containing four and two elements respectively such that $A\cap B=\varphi$. Then the number of subsets of set $A\times B$ each having at least five elements is

Answer 1

$n(A\times B)=8$
Number of subsets of $A\times B$ having at least $5$ elements will be
${}^8{C}_5+{}^8{C}_6+{}^8{C}_7+{}^8{C}_8={}^8{C}_3+{}^8{C}_2+{}^8{C}_1+{}^8{C}_0=56+28+8+1=93$