Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of $A × B$ having 3 or more elements is _____.
Answer & explanation
We have, n(A) = 2 and n(B) = 4
$∴n(A × B)=n(A)×n(B)=2×4=8$
The number of subsets of $A × B$ having 3 or more elements
${^8C}_3+{^8C}_4+{^8C}_5+{^8C}_7+{^8C}_8$
$=({^8C}_0+{^8C}_1+....+{^8C}_8)-({^8C}_0+{^8C}_1+{^8C}_2)$
$=2^8-(1+8+28)=219$