How many 3 letter combinations from 22 letters?

The first letter can be any one of 22. For each of these ...

The second letter can be any one of the remaining 21. For each of these ...

The third letter can be any one of the remaining 20.

So the number of different 3-letter line-ups is (22 x 21 x 20) = 9,240.

That's the answer if you care about the sequence of the letters, i.e. if you call ABC and ACB different.

If you don't care about the order of the 3 letters ... if ABC, ACB, BAC, BCA, CAB, and CBA are all

the same to you, then there are six ways to arrange each group of 3 different letters.

Then the total number of different picks is (9,240/6) = 1,540.