Question

Let A and B be two sets containing four and two elements respectively. Then the number of subsets of the set $A\times B$ each having at least three elements is:
(IIT JEE Main 2015)

• A. 219
• B. 256
• C. 275
• D. 510

Answer 1

The correct option is A 219

Number of elements in Set A = 4
Number of elements in Set B = 2
$\therefore$ Number of elements in set (A $\times$ B) = 4 $\times$ 2 = 8
$\therefore$ Total number of subsets of (A $\times$ B) = $2^8=256$
Number of subsets having 0 elements = ${}^8{C}_0=1$
Number of subsets having 1 element each = ${}^8{C}_1=8$
Number of subsets having 2 elements each = ${}^8{C}_2=28$
Number of subsets having at least 3 elements = 256-1-8-28 = 219