Rich G. answered • 06/27/18

Tutor

5.0
(140)
Adjunct instructor, IXL video contributor

It's really low, that's why it's the highest ranked hand in poker.

The number of possible 5 card combinations in a deck of cards is

_{52}C

_{5}= 52!/5!(52-5)! = 52!/(5!*47!) = 2,598,960 possible combinations

There are only 4 possible combinations of a royal flush

So the odds of being dealt a royal flush is

4/2,598,960

= 1.539 * 10

^{-6}Or 1 out of 649,740