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 flushes = Possible ways to get 5 of the same suit.

Possible flushes in one suit * 4 suits = 13! * 4/((13 - 5)! * 5!) = 5,108 ways

Total Possible flushes * 4 possible suits = (13 * 12 * 11 * 10 * 9 * 4) / (5 * 4 * 3 * 2 * 1)

Possible flushes - (36 straight . 4 Royal {Flushes}) = (617,760 / 120) - 40

Possible flushes = 5,148 - 40

Possible flushes = 5108

Probability of a flush = | Possible flushes |

Total Possible 5 Card Hands |

Probability(Flush) = | 5,108 |

2,598,960 |

Using our GCF Calculator, we see that 5108 and 2598960 can be reduced by 4

Probability(Flush) = | 1,277 |

649,740 |

In decimal format, this probability is equal to approximately