From a deck of 52 cards, we want the number of possible unique ways we can

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) |

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

120 |

Total Possible 5 Card Hands = 2,598,960

Possible 4 of a kinds = Possible ways to get 4 cards of one kind and any 5th card

Possible 4 of a kinds = 13 different 4 of a kind choices * 48 remaining 5th cards = 624

Probability of a 4 of a kind = | Possible 4 of a kind hands |

Total Possible 5 Card Hands |

Probability(4 of a kind) = | 624 |

2,598,960 |

Using our GCF Calculator, we see that 624 and 2598960 can be reduced by 624

Probability(4 of a kind) = | 1 |

4,165 |

In decimal format, this probability is equal to approximately