Probability of 5 of a kind for (1-6) = Probability[All(1) + All(2) + All(3) + All(4) + All(5) + All(6)]

Probability of All Die = 1 = (1,1,1,1,1)

Probability of All Die = 1 = 1/6 * 1/6 * 1/6 * 1/6 * 1/6

Probability of All Die = 1 = | 1 |

7,776 |

Probability of All Die = 2 = (2,2,2,2,2)

Probability of All Die = 2 = 1/6 * 1/6 * 1/6 * 1/6 * 1/6

Probability of All Die = 2 = | 1 |

7,776 |

Probability of All Die = 3 = (3,3,3,3,3)

Probability of All Die = 3 = 1/6 * 1/6 * 1/6 * 1/6 * 1/6

Probability of All Die = 3 = | 1 |

7,776 |

Probability of All Die = 4 = (4,4,4,4,4)

Probability of All Die = 4 = 1/6 * 1/6 * 1/6 * 1/6 * 1/6

Probability of All Die = 4 = | 1 |

7,776 |

Probability of All Die = 5 = (5,5,5,5,5)

Probability of All Die = 5 = 1/6 * 1/6 * 1/6 * 1/6 * 1/6

Probability of All Die = 5 = | 1 |

7,776 |

Probability of All Die = 6 = (6,6,6,6,6)

Probability of All Die = 6 = 1/6 * 1/6 * 1/6 * 1/6 * 1/6

Probability of All Die = 6 = | 1 |

7,776 |

Probability of Yahtzee = | 1 + 1 + 1 + 1 + 1 + 1 |

7,776 |

Probability of Yahtzee = | 6 |

7776 |

Using our GCF calculator, we reduce top and bottom by 6, to get

Probability of Yahtzee = | 1 |

1,296 |