The permutation function is defined as:

P(n,k) =

*Examples*:

P(6, 3) |
= | = = = 6(5)(4) = 120. | |

P(9, 2) |
= | = = = 9(8) = 72. | |

P(7, 1) |
= | = = 7 | |

P(10, 10) |
= | = = = 10! = 3628800. |

The permutation function yields the number of ways that
*n*
distinct items can
be arranged in
*k*
spots. For example,
*P*(7, 3) = = 210
. We can
see that this yields the number of ways 7 items can be arranged in 3 spots --
there are 7 possibilities for the first spot, 6 for the second, and 5 for the
third, for a total of 7(6)(5):

P(7, 3) = = 7(6)(5) .

*Example*: The coach of a basketball team is picking among 11 players for
the 5 different positions in his starting lineup. How many different lineups
can he pick?

P(11, 5) = = = 55440 different lineups.

The combination function is defined as:

C(n,k) =

*Examples*:

C(6, 3) |
= | = = 20. | |

C(9, 2) |
= | = = 36. | |

C(7, 1) |
= | = = 7. | |

C(10, 10) |
= | = = 1. |

The combination function yields the number of ways
*n*
distinct items can be
chosen for
*k*
spots, when the order in which they are chosen does
not matter--that is, choosing ABCDE is equivalent to choosing BAEDC. In other words, we use
the combination function when all spots are equivalent.

*Example*: If Jim has 12 shirts, and needs to pack 7 for vacation, how
many different combinations of shirts can he pack?

C(12, 7) = = 792 different combinations of shirts.