Multi deck combinations help

I worked out some combinations, but I'm not 100% sure. I have a pan 9 game with the 7,8,9, and 10's removed. This leaves me with A-6 and jack,queen,king. There is also 8 decks.
I'm figuring out the three card poker combinations for a straight flush, three of a kind, straight, flush, pair, and nothing. I know total combinations is C(288,3), but the multi decks throw me off with individual totals and I'm hoping someone can do the math so I can check my work. Thanks.

Why don't you post your numbers first? What are you counting for straights? A23, 234, 345, 456, JQK, QKA

Yes. There are those straights. Here are my numbers

Straight flush 12288
Three of a kind 44640
Straight 184320
Flush 224256
Pair 1076400
Nothing 2398032

Quote: ikusa

Yes. There are those straights. Here are my numbers

Straight flush 12288
Three of a kind 44640
Straight 184320
Flush 224256
Pair 1076400
Nothing 2398032

Your pairs and nothing are of by 1872.
Pairs= 9*combin(32,2)*8*32 - 9*4*combin(8,2)*8*8

Thank you. I even had that number for my pairs originally, but thought it was wrong. I was actually more worried about the straights, but they must be right if we both got the same number. Thanks for all your help.