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

Calculate P(Royal Flush)

##### Royal Flush Hands

##### 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** |

GCF for 1 and 649740 = 4

P(Royal Flush) = | **1** |

| **649,740** |

##### Final Answer

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

_{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

##### Example calculations for the 5 Card Poker Hand Calculator

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