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**gcolby1****Member**- Registered: 2013-08-12
- Posts: 2

Great site. I took statistics and probability at UCLA, but am still unsure of a formula for my friend -- who runs a frozen yogurt shop! There are 7 flavors, 9 fruit toppings, 12 dry toppings, and 4 wet toppings (25 toppings total). Assume you can pick *two flavors* of yogurt (any two of the 7, repeat is ok I suppose), and then pick three toppings in any combination (repeating is ok I guess), how many combinations can he offer customers?? Help with that one would be great!

Thanks,

Colby

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,238

Hi gcolby1;

I am not sure that the problem is stated in the way that I understand it.

There are 7 flavors and you can repeat so that would be 7^2 = 49 but the order of them probably does not count. For instance chocolate and vanilla is the same as vanilla chocolate. So there are 28 ways to pick the 7 flavors.

The toppings are the same. I can triple up on the same one so 25^3 = 15625 but the order again does not count. So I can have 2925 of them.

Now we just multiply:

28 x 2925 = 140400 different combinations.

Welcome to the forum.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**gcolby1****Member**- Registered: 2013-08-12
- Posts: 2

BobbyyodaM, thank you. I think that's in the right ball park.

Now it's awesome, because if he lets you have two flavors in a small, but up to 4 in a large, let's see, that's 7^4 where the order doesn't count, is 56? so

for four flavors,

56 x 2925 = 163,800 different combinations?

and for one flavor,

7 x 2925 =20,475?

That's a lot of combinations!! I almost always go for blueberries for the health and flavor, and nuts for similar -- so my combinations are really in the hundreds. but I/m sure he'll be thrilled if I make a chart for him to display.

Thanks!!

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,238

Hi;

That is not correct. For four flavors in a large there are 210 ways to pick the 7 toppings.

210 x 2925 = 614250

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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