Well yes, but I don't think the object here was to do anything useful Scrabble-wise. We're just playing with letter combinations. If we WERE trying to do something useful, we would generate letter sets and match them up with dictionary words, rather than just counting the number of possible letter combinations.

That's even easier to do, given a file of dictionary words.

EDIT: I would like to add that if you have a small number of blanks (in this case, 2 or less), it is also possible to calculate the number of letter combinations from formulas. For 2 blanks:

Calculate number of letter sets with all unique letters
Calculate number of letter sets with one letter pair
Calculate number of letter sets with two letter pairs
Calculate number of letter sets with one letter triplet

Then you just need to calculate how many letter combinations can be made in each of the above cases for each letter set, multiply it out, and add up the results.