this is a probability question, just checking its right :)

Question

From a normal (shuffled) deck of cards, five cards are drawn. What is the probability that the draw will be a Royal Flush (Ace, King, Queen, Jack, 10 of the same suit) ?

Answer 1

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

 

₅₂C₅ = 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