Here's a math to get a royal flush.
To -start with, you have a 20/52 chance of getting any card you need in a flush. Then, you have 4/51 3/50 2/49 and 1/48. So, once you multiply them all together, you get 1/649740. If you want to know the odds for getting a Royal Flush in a particular suit, say, hearts, it would be that number divided by 4. Which is 1/2598960.
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