The formula for a combination of choosing

_{n}C_{r} = | n! |

r!(n - r)! |

where n is the number of items and r is the unique arrangements.

_{12}C_{11} = | 12! |

11!(12 - 11)! |

Remember from our factorial lesson that n! = n * (n - 1) * (n - 2) * .... * 2 * 1

n! = 12!

12! = 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

12! = 479,001,600

(n - r)! = (12 - 11)!

(12 - 11)! = 1!

1! = 1

1! = 1

r! = 11!

11! = 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

11! = 39,916,800

_{12}C_{11} = | 479,001,600 |

39,916,800 x 1 |

_{12}C_{11} = | 479,001,600 |

39,916,800 |