Combinations
A combination is an arrangement of objects without repetition where order is not important.
Note: The difference between a permutation and a combination is not whether there is repetition or not -- there must not be repetition with either, and if there is repetition, you can not use the formulas for permutations or combinations. The only difference in the definition of a permutation and a combination is whether order is important.
A combination of n objects, arranged in groups of size r, without repetition, and order being important is:
nCr = C(n,r) = n! / ( (n-r)! * r! )
Another way to write a combination of n things, r at a time is using the binomial notation:
AB = BA AC = CA BC = CB
There are only three two-letter combinations.
Shortcut formula for finding a combination
Assuming that you start a n and count down to 1 in your factorials ...
C(n,r) = first r factors of n factorial divided by the last r factors of n factorial
