Forum:SLASH'EM Mall - maximum number of shops?

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Does anyone know what the maximum number of shops in the SLASH'EM mall is? I have the probability table list that shows the maximum theroretical number of shops is 11, and the level layout has room for 11 shops. But in reality the most I've seen is 6. Maybe someone who knows more about combinatronics & statistics can calculate the total probability of getting any given number of shops. Here's the probability table:

General - 100% Tool - 20% Food - 40% Scroll- 20% Potion - 30% Ring - 12% Lighting - 33% Book - 12% Wand - 17% Weapon - 20% Armor - 22% --Preceding unsigned comment added by Alpheus (talkcontribs) 13:47, 29 October 2013

(Please remember to sign your edits to discussion pages with four tildes. Also, "combinatronics" sounds really fun, though I suppose you meant combinatorics :P)
It should obviously be possible for 11 shops to be generated, but it's not very likely. These should be the probabilities, unless I made some mistake:
Shops Probability (%; rounded) Probability (fraction; exact)
3 30.253880% 7386201181/24414062500
4 23.550969% 22998993511/97656250000
2 22.373073% 1365543993/6103515625
5 11.701577% 5713660551/48828125000
1 7.223241% 2204358156/30517578125
6 3.881733% 75815098907/1953125000000
7 0.871425% 1702001729/195312500000
8 0.130814% 255495747/195312500000
9 0.012573% 12277899/97656250000
10 0.000699% 2729727/390625000000
11 0.000017% 166617/976562500000
0 0% 0/1
bcode talk | mail 16:59, 30 October 2013 (UTC)