The Permutation Function
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
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. 
