Question

Let A and B be two sets containing four and two elements respectively. Then, the number of subset of the each having at least three elements are

• A. $219$
• B. $256$
• C. $128$
• D. $248$

Answer 1

The correct option is A $219$

A)

Set A has 4 elements

Set B has 2 elements

Number of elements in set (A x B) = 4 x 2 = 8

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

Number of subsets having 0 elements = 8c0 = 1

Number of subsets having 1 element each = 8c1 = 8

Number of subsets having 2 elements each = 8c2= 8!/(2!6!)=8*7/2=28

Number of subsets having at least 3 elements

= 256 - 1 - 8 - 28 = 256 - 37 = 219

So the answer is 219.