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In a standard 5-card poker hand for 1 deck:

Calculate P(Royal Flush)

##### Calculate Total 5 Card hands

Choose 5 cards from 52 cards

 Total Hands  = 52! (52-5)! * 5!

 Total Hands  = 52! 47! * 5!

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

##### Cancelling the 47!, we get:

 Total Hands  = 311,875,200 120

Total Hands = 2,598,960

##### Build Probability

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

 P(Royal Flush)  = Royal Flushes Total Hands

 P(Royal Flush)  = 4 649,740

##### Reduce top and bottom by 4

GCF = Greatest Common Factor

 P(Royal Flush)  = 4 2,598,960

 P(Royal Flush)  = 1 649,740

Decimal probability = 1.5391E-6

##### What is the Answer?
Decimal probability = 1.5391E-6
##### How does the 5 Card Poker Hand Calculator work?
Free 5 Card Poker Hand Calculator - Calculates and details probabilities of the 10 different types of poker hands given 1 player and 1 deck of cards.
This calculator has 1 input.

### What 1 formula is used for the 5 Card Poker Hand Calculator?

Total Possible 5 Card Hands = 2,598,960

For more math formulas, check out our Formula Dossier

### What 4 concepts are covered in the 5 Card Poker Hand Calculator?

5 card poker hand
combination
a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter
nPr = n!/r!(n - r)!
factorial
The product of an integer and all the integers below it
probability
the likelihood of an event happening. This value is always between 0 and 1.
P(Event Happening) = Number of Ways the Even Can Happen / Total Number of Outcomes