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.

_{15}C_{10} = | 15! |

10!(15 - 10)! |

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

n! = 15!

15! = 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

15! = 1,307,674,368,000

(n - r)! = (15 - 10)!

(15 - 10)! = 5!

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

5! = 120

r! = 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

_{15}C_{10} = | 1,307,674,368,000 |

3,628,800 x 120 |

_{15}C_{10} = | 1,307,674,368,000 |

435,456,000 |