There are fifteen nonempty subsets of the set (2,0,1,8). for each of these subsets, consider the sum of its elements. compute the number of different sums.

0

1

2

8

1+2=3

1+8=9

2+8=10

2+1+8=11

0 doesn't change the value of the sum, so we don't take into consideration subsets with 0 in it, except the subset with just 0 itself.

Therefore, there are 8 different sums.