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# News from Mathnasium of Dale City

### Here's the Scoop

Jul 17, 2019

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 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

Now I can pick a different starting flavor and do the same thing. Let’s try Mint Stracciatella.

I can have:

• Mint Stracciatella and Vanilla
• Mint Stracciatella and Cookies & Cream
• Mint Stracciatella and Espresso Biscotto
• Mint Stracciatella and M&M Birthday Cake
• Mint Stracciatella and Caramel
• Mint Stracciatella and Reese’s Cup
• Mint Stracciatella and Chocolate
• Mint Stracciatella and White Chocolate Grisbi
• Mint Stracciatella and Coconut
• Mint Stracciatella and Butter Pecan
• Mint Stracciatella and Hazelnut
• Mint Stracciatella and Cherry Cheesecake
• Mint Stracciatella and Chocolate Sorbet
• Mint Stracciatella and Pineapple Basil
• Mint Stracciatella and Lemon
• Mint Stracciatella and Strawberry
• Mint Stracciatella and Blackberry + Raspberry

But wait… Vanilla and Mint Stracciatella is the same as Mint Stracciatella and Vanilla 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.

• Chocolate and Vanilla
• Chocolate and Cookies & Cream
• Chocolate and Espresso Biscotto
• Chocolate and M&M Birthday Cake
• Chocolate and Caramel
• Chocolate and Reese’s Cup
• Chocolate and Cherry Cheesecake
• Chocolate and White Chocolate Grisbi
• Chocolate and Coconut
• Chocolate and Butter Pecan
• Chocolate and Hazelnut
• Chocolate and Mint Stracciatella
• Chocolate and Chocolate Sorbet
• Chocolate and Pineapple Basil
• Chocolate and Lemon
• Chocolate and Strawberry
• Chocolate 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.