Math Is Fun Forum

gcolby1

Member

Registered: 2013-08-12

Posts: 2

Combinations available... for frozen yogurt?! (Vanilla & Coconut...)

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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Combinations available... for frozen yogurt?! (Vanilla & Coconut...)

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gcolby1

Member

Registered: 2013-08-12

Posts: 2

Re: Combinations available... for frozen yogurt?! (Vanilla & Coconut...)

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!!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Combinations available... for frozen yogurt?! (Vanilla & Coconut...)

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.