Actually, there are 156 combinations with the final 9 items. With 6 items there are ((6 | 3)) = (6 + 3 - 1 | 3) = 8! / 6! = 8 * 7 = 56 combinations. See wikipedia.
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good to know, I didn't remember that the order doesn't count. But even with only 56 combination it's not so easy to try every combination. You still have to buy 3*56 ingredients one by one... I'm not complaining about the number itself, but the fact that I honestly gave up because it was to repetitive to try without an hint on the ingredients.
There was a plan for a while to have descriptions for the ingredients to make it more possible to figure out recipes, for instance the darkvision potion contains both rat tail and newt eye (rats can see in the dark) and flight potion will contain dragonfly wings and fairy dew (both dragonflies and fairies can fly). however I didn't have enough time in the end to get that worked out. I also wanted to have a recipe book to show what potions it was possible to find, but that also got scrapped. Being able to buy ingredients in bulk would definitely have made sense to add as a feature.