Distinguishable Permutations
Sometimes letters are repeated and all of the permutations aren't distinguishable from each other.
Example: Find all permutations of the letters "BOB"
To help you distinguish, I'll write the second "B" as "b"
BOb BbO OBb ObB bBO bOB
If you just write "B" as "B", however ...
BOB BBO OBB OBB BBO BBO
There are really only three distinguishable permutations here.
BOB BBO OBB
If a word has N letters, k of which are unique, and you let n (n1, n2, n3, ..., nk) be the frequency of each of the k letters, then the total number of distinguishable permutations is given by:
Consider the word "STATISTICS":
Here are the frequency of each letter: S=3, T=3, A=1, I=2, C=1, there are 10 letters total
10! 10*9*8*7*6*5*4*3*2*1
Permutations = -------------- = -------------------- = 50400
3! 3! 1! 2! 1! 6 * 6 * 1 * 2 * 1
