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Home : Math & Science : Math Study Guides : Algebra II : Discrete Functions : Permutations and Combinations
Permutations and Combinations
The Permutation Function
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):
= 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).
= 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.
= = 55440 different lineups.
The Combination Function
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.
= 792 different combinations of shirts.
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