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_{5} = | 12! |

5!(12 - 5)! |

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 - 5)!

(12 - 5)! = 7!

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

7! = 5,040

r! = 5!

5! = 5 x 4 x 3 x 2 x 1

5! = 120

_{12}C_{5} = | 479,001,600 |

120 x 5,040 |

_{12}C_{5} = | 479,001,600 |

604,800 |