Odds of a flush

A flush is determined by the suit and the rank combos (the number of possible hands from a deck where three suits have been removed). The number of rank combos are calculated similarly to the total number of 5-card hands. There are 13*12*11*10*9 arranged hands. We divide by the number of arrangements (5*4*3*2*1) to get 1287 rank combos.

n(flushes) = suit combos * rank combos = 4 suits * 1287 flushes/suit = 5148 flushes

This number includes straight flushes, so there are 5108 ordinary flushes. These flushes can be divided into ace-high, king-high and so on. I might come up with numbers for those categories later.