If you’re anything like me, you have a hard time deciding on just two flavors when you go out for ice cream. There are so many flavors and so many combinations!
It begs the question, how many flavor combinations are there?
Let’s start by picking one flavor and seeing how many other flavors I can pair with it. We’ll start with Reese’s Cup.
I can have:
- Reese’s Cup and Vanilla
- Reese’s Cup and Cookies & Cream
- Reese’s Cup and Espresso Biscotto
- Reese’s Cup and M&M Birthday Cake
- Reese’s Cup and Caramel
- Reese’s Cup and Chocolate
- Reese’s Cup and Cherry Cheesecake
- Reese’s Cup and White Chocolate Grisbi
- Reese’s Cup and Coconut
- Reese’s Cup and Butter Pecan
- Reese’s Cup and Hazelnut
- Reese’s Cup and Mint Stracciatella
- Reese’s Cup and Chocolate Sorbet
- Reese’s Cup and Pineapple Basil
- Reese’s Cup and Lemon
- Reese’s Cup and Strawberry
- Reese’s Cup and Blackberry + Raspberry
That’s 17 combinations already!
Now I can pick a different starting flavor and do the same thing. Let’s try Vanilla.
I can have:
- Vanilla and Lemon
- Vanilla and Cookies & Cream
- Vanilla and Espresso Biscotto
- Vanilla and M&M Birthday Cake
- Vanilla and Caramel
- Vanilla and Reese’s Cup
- Vanilla and Cherry Cheesecake
- Vanilla and White Chocolate Grisbi
- Vanilla and Coconut
- Vanilla and Butter Pecan
- Vanilla and Hazelnut
- Vanilla and Mint Stracciatella
- Vanilla and Chocolate Sorbet
- Vanilla and Pineapple Basil
- Vanilla and Chocolate
- Vanilla and Strawberry
- Vanilla and Blackberry + Raspberry
But wait… Reese’s Cup and Vanilla is the same as Vanilla and Reese’s Cup right? The order doesn’t really matter to me. So I want to make sure I’m not counting doubles when I’m counting. That means I’ll actually have one less combination this time.
If I do that again, I’ll again have my list of all combinations, but this time I can cross two doubles out.
- Coconut and Vanilla
- Coconut and Cookies & Cream
- Coconut and Espresso Biscotto
- Coconut and M&M Birthday Cake
- Coconut and Caramel
- Coconut and Reese’s Cup
- Coconut and Cherry Cheesecake
- Coconut and White Chocolate Grisbi
- Coconut and Chocolate
- Coconut and Butter Pecan
- Coconut and Hazelnut
- Coconut and Mint Stracciatella
- Coconut and Chocolate Sorbet
- Coconut and Pineapple Basil
- Coconut and Lemon
- Coconut and Strawberry
- Coconut and Blackberry + Raspberry
If this pattern continues, then each time I’ll have one less pair to count. So instead of listing them out every time I can use this pattern to get my answer faster!
17 + 16 + 15 + 14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 153 different combinations!
All that math has made me hungry! I think I’ll get White Chocolate Grisbi and Lemon.
