Let A and B be two sets containing four and two elements respectively. Then the number of subsets of the set A × B , each having at least three elements is

Step-by-step solution

Given n A = 4 n B = 2 Number of elements in n A   ×   B = 2 × 4 = 8 Number of subsets = 2 8 Number of subsets having less than 3 elements = 8 C 0 + C 8 1 + C 8 2 Number of subsets having at least 3 elements = 2 8 - 8 C 0 - C 8 1 - C 8 2 = 256 - 1 - 8 - 28 = 219