Probability of Royal Flush

                   

 → 

---

Calculate the probability of a Royal Flush:

First calculate the total number of possible hands in a 52 card deck:
From a deck of 52 cards, we want the number of possible unique ways we can choose 5 cards.
Using the combinations formula 52 choose 5 shown here, we get:

Total Possible 5 Card Hands  =	52!
	(52-5)! * 5!

Total Possible 5 Card Hands  =	52!
	47! * 5!

Total Possible 5 Card Hands  =	(52 * 51 * 50 * 49 * 48) * 47!
	47! * (5 * 4 * 3 * 2 * 1)

Cancelling the 47! on top and bottom we get:

Total Possible 5 Card Hands  =	311,875,200
	120

Total Possible 5 Card Hands = 2,598,960

Possible Royal Flushes = Possible ways to get 10,J,Q,K,A all suited
Possible Royal Flushes = 1 way * 4 possible suits (Spade,Heart,Diamond,Club) = 4

Probability(Royal Flush)  =	Possible Royal Flushes
	Total Possible 5 Card Hands

Probability(Royal Flush)  =	4
	2,598,960

Using our GCF Calculator, we see that 4 and 2598960 can be reduced by 4
Reducing top and bottom by 4, we get:

Probability(Royal Flush)  =	1
	649,740

---

Run Another Calculation