I will assume with the title of your thread that we don't need "unique" arrangements, we are dealing with groups of 3 choosing from a pool of 18: That answer is 4,896.

Go here:

Permutation and Combination Calculator

Number of Items is 18, Arrangements is 3. This is read as 18 choose 3.

If in fact I am incorrect in my assumption, and we need unique arrangements, press the combination button instead. That would be read as 18 choose 3 unique. That answer would be 816.

Either way will show you the math work for your answer

Think of it as having 18 people, 1-18. We take groups of 3, such as (1,2,3), (4,5,6), etc. For arrangements that do not need to be unique, (1,2,3) is considered different than (3,2,1). For unique arrangements, i.e., combinations, (1,2,3) is considered the same as (3,2,1) so that type is only counted once.

Any questions?