How many possible ways can this be done? (A,B,C,D,E)

[pwange]

Example:
1. (A,B,C,D,E)
2. (A,B,C,D)
3. (A,B,C)
4. (A,B)
5. (A)
6. (A,B,D,E)
etc...
I just put it in a table format, as it's easier to count this way (31 columns = 31 solutions).
Not sure if there are any more ways to do this.

Questions:

1) Are there only 31 ways to do this?

2) Is there like a calculator online which solves this sort of problem?

3) Is there a name for this sort of problem?

 

[Greg]

It appears you want A, B, C, D and E arranged in alphabetical order with at least one letter present. There are $2^5-1 = 31$ ways to do this; we subtract $1$ to omit the configuration of having all blanks. The $2^5$ comes from the number of possibilities for each "slot", which is $2$: a letter or a blank.