I've been working on probability problems because of final exams this week so to be honest I don't really know how many times you could re-arrange this..
I dont know what you mean with 'distinct' but: there's 11 letters, which basically means It's 11! (11 factorial).
11!=11*10*9*8*7*6*5*3*2*1=39916800. This is including the word Tallahassee.
And this is not probability, It's combinatorics.