Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

## #1 2013-08-13 08:58:45

gcolby1
Novice

Offline

### 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

## #2 2013-08-13 09:49:58

bobbym

Offline

### 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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #3 2013-08-21 08:50:30

gcolby1
Novice

Offline

### 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!!

## #4 2013-08-21 09:05:29

bobbym

Offline

### 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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.