On Saturday, May 10, 2014 8:21:28 AM UTC-4, radam...@gmail.com wrote: > Thought experiment: > > > > Lets say that I randomly draw N letters out of a Scrabble letter-bag. I will then place those letters in a horizontal line on a table. How many UNIQUE patterns of letters can I produce? If there were no duplicates it would be easy (N factorial) but when there are duplicate letters it seems more complicated. > > > > Bob
For any specific set of N letters it is trivial:
where #A = the number of A's occurring in the string, etc. Most factors in the denominator are of the form 0! = 1 or 1! = 1 and can be omitted.
For example there are 11!/(4!4!2!) distinguishable permutations of MISSISSIPPI since #I = 4, #S = 4, #P = 2
If you are talking about random collections of N tiles drawn from a standard set of Scrabble tiles then the number of distinguishable permutations becomes a random variable. It would most likely require a computer to enumerate the range of this random variable, calculate its expected value, etc.