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.

_{7}C_{4} = | 7! |

4!(7 - 4)! |

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

n! = 7!

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

7! = 5,040

(n - r)! = (7 - 4)!

(7 - 4)! = 3!

3! = 3 x 2 x 1

3! = 6

r! = 4!

4! = 4 x 3 x 2 x 1

4! = 24

_{7}C_{4} = | 5,040 |

24 x 6 |

_{7}C_{4} = | 5,040 |

144 |