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How we get to 2,598,960
There are 2,598,960 hand combinations in a five card poker hand. You will get that number by multiplying 52 cards out of five, 51 out of four, 50 out of three, 49 out of two and 48 out of 1. 52/5 x 51/4 x 50/3 x 49/2 x 48/1 = 2,598,960. This is how many different hand combinations that you can have when factoring that a Ah Kh 8s 9s 5h is the same hand as Kh 9s 5h 8s Ah. Otherwise there would be 311,875,200 different hand combinations.
7-Card Stud combinations
There are 133,784,560 hand combinations in a seven card poker hand. There are 4324 royal flush possibilities. 4 x 47/2 x 46/1 = 4324.
There are 37260 straight flush possibilities. 4 suits x 9 different straight flushes x 46/2 x 45/1 = 37260. It is harder to get a particular straight flush, than a royal flush, because you must make the best hand possible out of the cards that you have. Which means that there are fewer combinations of leftover cards for a regular straight flush.
There are 224,848 four of a kind combinations. You can figure this out by having (13 different four of a kinds x 48/3 x 47/2 x 46/1) = 224,848.