Try VLookup or Match/Index functions assuming each selection of Vanilla (6), Chocolate (7), Strawberry (8), etc. has the same number of elements.

In a reference table, have flavors and reference values in adjacent cells (6, 7, 8, etc.). In a lookup table, have those same reference values with elements to the right.
=Vlookup("Vanilla",<reference table>,<column 2>,<true/false>)
the result would be 6
Then you could us
= Index(<lookup table>,<row - from reference table>, <column 1...4 - for elements>)

I hope that was simple and complete enough to point you in the right direction. If you use formulas in Excel, you can start with =VLookup(... and get the data needed for the formulas.

EXTRAS:
You can combine both tables into one on a hidden sheet and use that to enable your pick list of flavors and the results that get displayed.
You can also define name ranges for your tables to make for simpler formulas
If the number of elements/ingredients vary with the selection, that's possible too, but you may need to get more creative with how you manage reference values