Probability of 4 of a kind = Probability[4(1s or 2s or 3s or 4s or 5s or 6s & unequal 5th die)]

Probability of 4 1's = All possibilities of 4 1's & unequal 5th die * 6 die faces

P(1,1,1,1,not 1) = 1/6 * 1/6 * 1/6 * 1/6 * 5/6

P(1,1,1,1,not 1) = | 5 |

7,776 |

Probability of 4 2's = All possibilities of 4 2's & unequal 5th die * 6 die faces

P(2,2,2,2,not 2) = 1/6 * 1/6 * 1/6 * 1/6 * 5/6

P(2,2,2,2,not 2) = | 5 |

7,776 |

Probability of 4 3's = All possibilities of 4 3's & unequal 5th die * 6 die faces

P(3,3,3,3,not 3) = 1/6 * 1/6 * 1/6 * 1/6 * 5/6

P(3,3,3,3,not 3) = | 5 |

7,776 |

Probability of 4 4's = All possibilities of 4 4's & unequal 5th die * 6 die faces

P(4,4,4,4,not 4) = 1/6 * 1/6 * 1/6 * 1/6 * 5/6

P(4,4,4,4,not 4) = | 5 |

7,776 |

Probability of 4 5's = All possibilities of 4 5's & unequal 5th die * 6 die faces

P(5,5,5,5,not 5) = 1/6 * 1/6 * 1/6 * 1/6 * 5/6

P(5,5,5,5,not 5) = | 5 |

7,776 |

Probability of 4 6's = All possibilities of 4 6's & unequal 5th die * 6 die faces

P(6,6,6,6,not 6) = 1/6 * 1/6 * 1/6 * 1/6 * 5/6

P(6,6,6,6,not 6) = | 5 |

7,776 |

Probability of 4 of a kind = All possible of 4 of a kinds & unequal 5th die * 6 die faces

Probability of 4 of a kind = | (5 + 5 + 5 + 5 + 5) x 6 die faces |

7,776 |

Probability of 4 of a kinds = | 25 x 6 die faces |

7,776 |

Probability of 4 of a Kind = | 150 |

7776 |

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

Probability of 4 of a Kind = | 25 |

1,296 |