Hi all, first time here so I hope I'm in the right place. If not then an indication of where this should go would be great.
The situation is this: I have 11 variables, each with 5 possible states, 0 through to 4. The probability of each variable being in each state is different:
0 is 0.314055
1 is 0.425012
2 is 0.211677
3 is 0.045687
4 is 0.003568
With 11 variables each being 0 to 4 then there are a total of 45 different "total" states, i.e. the sum of the states for each variable can range from 0 (all at state 0) to 44 (all at state 4).
While it is easy enough to work out how many permutations will give us each state, what I am trying to calculate is the probability for each "total" state, e.g. what is the probability of the sum of the states being 22 (or whatever). Any ideas other than the long way of going through each permutation?