Question

A has 5 elements and B has 2 elements. The number of subsets of A×B such that the number of elements in subset is more than or equal to 3 and less than 6, is?

• A. 602
• B. 484
• C. 582
• D. 704

Answer 1

Answer: (C)

582

Answer 2

The set A × B contains a total of 5 × 2 = 10 elements. To form a subset of A × B with at least 3 and at most 5 elements, we can consider the following cases:
Case 1: Choose 3 elements from A × B
The number of ways to choose 3 elements from A × B is (10 choose 3) = 120.
Case 2: Choose 4 elements from A × B
The number of ways to choose 4 elements from A × B is (10 choose 4) = 210.
Case 3: Choose 5 elements from A × B
The number of ways to choose 5 elements from A × B is (10 choose 5) = 252.
Therefore, the total number of subsets of A × B with at least 3 and at most 5 elements is:
120 + 210 + 252 = 582
Hence, there are 582 such subsets.
Answer. C