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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. |
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