Hi, Don.
 
Thanks for the explanation. 
 
I'm probably missing something, but looking just at
our distinct integer expressions for the same
probability, it seems non-obvious that they are equal:
 
          109*108*...*92*91     126*124*122*120*...* 92
Why would -----------------  =  ----------------------- ?
          127*125*... 93*91     127*126*125*124*...*110
 
 
--Dan