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_{3} = | 12! |

3!(12 - 3)! |

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 - 3)!

(12 - 3)! = 9!

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

9! = 362,880

r! = 3!

3! = 3 x 2 x 1

3! = 6

_{12}C_{3} = | 479,001,600 |

6 x 362,880 |

_{12}C_{3} = | 479,001,600 |

2,177,280 |