Expert: Steve Holleran - 9/19/2008

Question
Assume that the set S has 14 elements. How many subsets of S have at most 2 elements?

Answer
Hi Nancy,


Okay, so to have at most 2 elements, that means

 0 elements or 1 element or 2 elements

0 elements = 1 subset (empty set)

1 element  = 14 subsets (each individual element)

2 elements = 14(C)2 = combination of 14 items, 2 at a time

          = 14! / (2! * 12!)= (14 * 13 * 12!) / (2! * 12!)

          = (14 * 13) / 2 = 91

So, I would say 1 + 14 + 91 = 106 subsets have at most 2 elements

Steve