I have the following permutation and combination related problem;

I have a deck of 84 cards made up of 7 unique types as follows;

Card #1: 18
Card #2: 12
Card #3: 6
Card #4: 6
Card #5: 18
Card #6: 18
Card #7: 6

9 cards are dealt to each player, and from thes 9 cards the player constructs a hand of 5 cards.

If I understand permutations correctly, from the 9 cards each player can construct 15120 possible permutations of cards. What I need to know is this; how many UNIQUE permutations and combination exist for any mixture of cards.

For example a player may have 2 of Card #1, 3 of Card #2, 1 of Card #3, 2 of Card #6, and 1 of Card #7. Of the 15120 possible permutations, many will be duplicates. How can I calculate how many duplicates will exist or, better yet, how many unique combinations exist?

Thank you.