The number of permutations
How many permutations does {a,b,c,d,e} have?
There are 5 ways to select the 1st term,
4 ways to select the 2nd term,
3 ways to select the 3rd term,
2 ways to select the 4th term,
1 way to select the 5th term
Total: 5?4?3?2?1 = 5! = 120 ways.
In general, the number of permutations of a set of n elements is
n ? (n-1) ? (n-2) ? … ? 1 = n!
The number of r-permutations of such a set is
n ? (n-1) ? (n-2) ? … ? (n-r+1) = n! / (n-r)!
This number is denoted by P(n,r).