When making a number combination from {1,2,3,4,5},

there are 2 choices for the 1, use it in the combination or don't use it.
there are 2 choices for the 2, use it in the combination or don't use it.
there are 2 choices for the 3, use it in the combination or don't use it.
there are 2 choices for the 4, use it in the combination or don't use it.
there are 2 choices for the 5, use it in the combination or don't use it.

That's 2×2×2×2×2 = 25 = 32

1.  {1,2,3,4,5}
2.  {1,2,3,4}
3.  {1,2,3,5}
4.  {1,2,3}
5.  {1,2,4,5}
6.  {1,2,4}
7.  {1,2,5}
8.  {1,2}
9.  {1,3,4,5}
10.  {1,3,4}
11.  {1,3,5}
12.  {1,3}
13.  {1,4,5}
14.  {1,4}
15.  {1,5}
16.  {1}
17.  {2,3,4,5}
18.  {2,3,4}
19.  {2,3,5}
20.  {2,3}
21.  {2,4,5}
22.  {2,4}
23.  {2,5}
24.  {2}
25.  {3,4,5}
26.  {3,4}
27.  {3,5}
28.  {3}
29.  {4,5}
30.  {4}
31.  {5}
32.  {}

Notice that the 32nd combination 
is a combination of NONE AT ALL!!!

Edwin