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 Strawberry.
I can have:
- Strawberry and Vanilla
- Strawberry and Cookies & Cream
- Strawberry and Espresso Biscotto
- Strawberry and M&M Birthday Cake
- Strawberry and Caramel
- Strawberry and Reese’s Cup
- Strawberry and Cherry Cheesecake
- Strawberry and White Chocolate Grisbi
- Strawberry and Coconut
- Strawberry and Butter Pecan
- Strawberry and Hazelnut
- Strawberry and Mint Stracciatella
- Strawberry and Chocolate Sorbet
- Strawberry and Pineapple Basil
- Strawberry and Lemon
- Strawberry and Chocolate
- Strawberry and Blackberry + Raspberry
That’s 17 combinations already!
Now I can pick a different starting flavor and do the same thing. Let’s try Blackberry + Raspberry.
I can have:
- Blackberry + Raspberry and Vanilla
- Blackberry + Raspberry and Cookies & Cream
- Blackberry + Raspberry and Espresso Biscotto
- Blackberry + Raspberry and M&M Birthday Cake
- Blackberry + Raspberry and Caramel
- Blackberry + Raspberry and Reese’s Cup
- Blackberry + Raspberry and Chocolate
- Blackberry + Raspberry and White Chocolate Grisbi
- Blackberry + Raspberry and Coconut
- Blackberry + Raspberry and Butter Pecan
- Blackberry + Raspberry and Hazelnut
- Blackberry + Raspberry and Mint Stracciatella
- Blackberry + Raspberry and Chocolate Sorbet
- Blackberry + Raspberry and Pineapple Basil
- Blackberry + Raspberry and Lemon
- Blackberry + Raspberry and Strawberry
- Blackberry + Raspberry and Cherry Cheesecake
But wait… Strawberry and Blackberry + Raspberry is the same as Blackberry + Raspberry and Strawberry 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.
- Lemon and Vanilla
- Lemon and Cookies & Cream
- Lemon and Espresso Biscotto
- Lemon and M&M Birthday Cake
- Lemon and Caramel
- Lemon and Reese’s Cup
- Lemon and Cherry Cheesecake
- Lemon and White Chocolate Grisbi
- Lemon and Coconut
- Lemon and Butter Pecan
- Lemon and Hazelnut
- Lemon and Mint Stracciatella
- Lemon and Chocolate Sorbet
- Lemon and Pineapple Basil
- Lemon and Chocolate
- Lemon and Strawberry
- Lemon 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.
