Let A and B be two sets containing four and two elements respectively

• Sets

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

1. 510
2. 256
3. 275
4. 219

Solution

n(A) = 4

n(B) = 2

n(A × B) = 8

So atleast 3 = total – none – one – two digits

= 28 – 1 – ⁸C₁ – ⁸C₂ = 28 – 1 – 8 – 28 = 28 – 37

= 256 – 37 = 219

The correct option is D.