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.

_{19}C_{2} = | 19! |

2!(19 - 2)! |

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

n! = 19!

19! = 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

19! = 121,645,100,408,832,000

(n - r)! = (19 - 2)!

(19 - 2)! = 17!

17! = 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

17! = 355,687,428,096,000

r! = 2!

2! = 2 x 1

2! = 2

_{19}C_{2} = | 121,645,100,408,832,000 |

2 x 355,687,428,096,000 |

_{19}C_{2} = | 121,645,100,408,832,000 |

711,374,856,192,000 |