How many three-letter code words can be constructed from the first ten letters of the greek alphabet if no repetitions are allowed?

Well, this is the wrong section as this is actually a maths question. To answer your question, though -- what you're looking for is a permutation. You have 9 symbols to choose from for the first letter, 8 symbols for the second (since you're already using one of them), and 7 symbols for the third (since you're already using two of them).