Talking about just beer strains? 15 would be better, for beer yeasts...
Wyeast:
1056
1084
1728
1335
1332
1450
1275
1968
Two each of the Belgian Ale strains and two lager strains..
For other yeast
Lalvin:
D47
EC-1118
71B-1122
RC 212
ICV K1V-1116
Also, I think limiting yourself to just 10 or 15 strains for any length of time wouldn't be good. Even if you only had a couple of the strains initially, to see what moves better. Also be prepared to special order yeast (post that you are willing/able to do that for people) and have it available within a week. I'm sure there are people that prefer White Labs as well as dry yeast over others. To not stock at least some of the strains would be a negative, IMO.
Anyway, if I was limited in what I could stock, the above is what I would stock... Luckily, the LHBS I get my yeast from isn't so limited. They have a lot of yeast strains on hand to pick from. If they don't have something I want, they can get it pretty fast. I typically go in at least the weekend before I need the yeast, in case they do need to order it up for me. Since they place their order on either Sunday or Monday, with it arriving that Thursday, it works out well.