You are stuck with "combinations" if you can't infer an order from the encoding. Simon's scheme effectively imposes an order as you "know" all of the colors can potentially be present -- or not. So, you can effectively order their presence or absence in your interpretation.
I suggested an implied ordering by using SILVER + colors vs. GOLD + colors -- in the hope that the marks would reliably be reported in the order encountered (even if that is the reverse of what you expect).
E.g., someone reporting the color bands on a resistor as GOLD BROWN BROWN VIOLET RED would still be understood as RED VIOLET BROWN BROWN GOLD.
Being able to use P(n,m) instead of C(n,m) greatly increases the number of different "encodings" available for any n & m.