If you are not aware, Sonic advertises that it has 168,894 drink combinations. Those of you that know about prime factorization and the fundamental counting principle might be raising your eyebrows at this number. Here is how this value is calculated.
First, take one of 13 drink bases. I can only assume from working there that the choice is probably between Coke, Diet Coke, Root Beer, Dr. Pepper, Sprite, Diet Sprite, Diet Dr. Pepper, Slush, Lemonade, Limeade, Cranberry Juice, Powerade, or Hi-C.
Then, add in between 0-6 of the 16 flavor add-ins. Note that one of the choices is already made for the last five drink bases, since that is required to make that drink. The flavor add-ins are: Chocolate, Cherry, Strawberry, Diet Cherry, Pineapple, Lemon, Lime, Blue Coconut, Grape, Orange, Powerade, Cranberry, Apple Juice, Vanilla, Hi-C, and Watermelon.
After taking all these combinations, we must subtract one, because nobody would want a Slush base with no add-in flavor. Nobody normal. But then, we add six for the drinks that don't get add-ins. I'm not sure which are the six, but Orange Juice, Apple Juice, Milk, Chocolate Milk are probably four. Maybe the other two are Hot Chocolate and Coffee. I'm just doing the math.
Anyway, this gives us our final result:
16C0 = 1
16C1 = 16
16C2 = 120
16C3 = 560
16C4 = 1820
16C5 = 4368
16C6 = 8008
= 14893*8 = 119144
15C0 = 1
15C1 = 15
15C2 = 105
15C3 = 455
15C4 = 1365
15C5 = 3003
15C6 = 5005
= 9949*5 = 49745
= 168889 + 6 - 1 =
= 168,894 drink combinations.
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