__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** |

In decimal format, this probability is equal to approximately **1.5391E-6**

### What is the Answer?

In decimal format, this probability is equal to approximately **1.5391E-6**

### How does the 5 Card Poker Hand Calculator work?

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

_{n}P_{r} = 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

### What are some example calculations for the 5 Card Poker Hand Calculator?

## Tags:

Add This Calculator To Your Website