Question

Let A and B two sets containing four and two elements respectively, The number of subsets of the set A × B, each having at least three elements is:
1. 270
2. 239
3. 219
4. 256

Answer 1

Correct Answer - Option 3 : 219

Concept:

Selection r things out of n things is denoted by nCr 

nCr = \(\rm \frac {n!}{(n-r)!r!}\)

 

Calculation:

Set A has 4 elements

Set B has 2 elements

Total number of element in (A × B) = 4 × 2 = 8

Total number of subsets of (A × B) = 2⁸ = 256

Number of subsets having 0 element = ⁸​C₀ ​= 1

Number of subsets having 1 element = ⁸​C₁​ = 8

Number of subsets having 2 elements = ⁸​C₂ ​= (8 × 7)/2 ​= 28

Number of subsets having at least 3 elements

= 256 – 28 – 8 – 1 = 219

Hence, option (3) is correct.