Combination

To understand the meaning of the formula of combination, we must understand permutation first.

Permutation:
Permutation is counting the number of methods to pick r things in n things while caring about the order. Example is 5P2:
12,13,14,15,21,23,24,25,31,32,34,35,41,42,43,45,51,52,53,54
Therefore 5P2=20.
The first thing to be picked has n cases, the second has n-1, the third has n-2, etc, and the r-th thing to be picked has n-r+1 cases.
Therefore, the formula is n*(n-1)*(n-2)*...*(n-r+1)! = n!/(n-r)!

Combination:
Combination is almost the same as permutation, except that we do not care about the order. There are r! ways to regroup the order, therefore we take away (divide) r! from the formula of permutation, forming the formula of combination:
n!/[(n-r)!r!]