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.

_{10}C_{4} = | 10! |

4!(10 - 4)! |

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

n! = 10!

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

10! = 3,628,800

(n - r)! = (10 - 4)!

(10 - 4)! = 6!

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

6! = 720

r! = 4!

4! = 4 x 3 x 2 x 1

4! = 24

_{10}C_{4} = | 3,628,800 |

24 x 720 |

_{10}C_{4} = | 3,628,800 |

17,280 |