Added by Wil on April 04, 2002 at 23:00:49:
Factorial: factorial equals n*(n-1)*(n-2)*(n-3)*(n-4)*(n-5) and so on until n-x=1. It is written n!. For example:
5! = 120
5*4=20, 5*4*3=60, 5*4*3*2=120, 5*4*3*2*1=120
so...
5*4*3*2*1=120 or 5!
Permutations: permutations are the number of things(n) taken (r) at a time. It is written nPr. For example:
nPn is n!
6P6 is 6*5*4*3*2*1 = 720
however...
6P3 is 6*5*4 = 120
It is 6!, but it stops after going around 3 times, not at the number 3.
8P5 = 8*7*6*5*4 = 6,720
Another way of looking at it is 8P5 = 8!/(8-5)!
Either way, same answer.
Combinations: are a way of looking at things without worrying what order they are in. For example, (A+B),(B+A):(A+C),(C+A):(A+D),(D+A and so on; now it looks like {B,A}:{C,A}:{D,A} and so on. The number of Combonations of (n) things taken (r) at a time is written nCr--nCr = nPr / r! For example:
4C2 = 4P2 / 2! or (4*3)/(2*1) or 12/2 or 6
7C5 = 7P5 / 5! or (7*6*5*4*3)/(5*4*3*2*1) or 2,520/120 or 21.