This seems more like a job for a frequency list. You can use a dictionary of characters and counts like so:
for each word in the dictionary
build a frequency list of each character initialized to 0
for each character in the letter collection
if the character exists in the frequency list
increment the count for that character
if all counts in the frequency list are greater than 0
mark the word as a match
You're basically just matching at least one of every letter in a given word using the available tiles that the player currently has. All of the words that meet this requirement are words that the player can make with his or her tiles.
Probably the easiest way is to put all the words in a TreeMap (for fast searching) then check every permutation of every subset of your letters to see if it's in the TreeSet. However that will generate a lot of searches if you have a lot of letters, which may or may not make it too slow.
You can speed up the search, at the cost of more work at startup time, by building a TreeMap. For each word sort its letters into order and use that as the key; the word (or words)corresponding to that form the value. Now you just need to test each subsets of your letters once - keep them sorted and see if the subset is a valid key. There's no need to test all the permutations.
Decepticon's solution may be faster or easier than either of these, but I'm ashamed to admit that I don't understand it.
OK, thank you. That seems functionally equivalent to creating a key that contains the letters in the word but sorted - ie its a way of identifying words that is independent of the order in which its letters appear. (Correct me if I'm wrong, please.)