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**infinitebrain****Member**- Registered: 2008-07-01
- Posts: 153

Hi guys again! I need help with this problem:

Berry Kold Creamery has four flavors of ice cream: vanilla, pistachio,black walnut, and strawberry.The daily sundae has three scoops of ice cream. How many variations of the sundae are there?

I don't need the numerical answer, I would just like how you would set the combination for the question to solve it.

Thanks!*Edited to explain more clearly, I hope this helps bobbym*

*Last edited by infinitebrain (2013-01-08 17:04:02)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,771

Hi;

I am not understanding the terminology.

A creamery has four flavors.The daily sundae has three scoops.

Four flavors of ice cream? Three scoops of what?

If you just want 3 scoops of the 4 flavors then there are

different types.

**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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**cooljackiec****Member**- Registered: 2012-12-13
- Posts: 160

The total ways of getting a three scoop cone would be:

This is because we can get multiple stuff of one flavor.

I see you have graph paper.

You must be plotting something

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,771

Hi cooljackie;

It is not that simple, there are 64 different sundaes if the order of the scoops counts 4 x 4 x 4 = 64 but only 20 if the order does not count.

**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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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,395

hi

Berry Kold Creamery has four flavors of ice cream: vanilla, pistachio,black walnut, and strawberry.The daily sundae has three scoops of ice cream. How many variations of the sundae are there?

To me, this means you can buy an ice cream called a daily sundae, which means you get three scoops of ice cream. You can choose the flavours for your scoops: so you could have all three different; or have some repeats. Order of repeats wouldn't matter; how you eat them is independent of the purchase order!

So I'll split the problem according to how many repeats.

(i) No repeats: I can choose 4, then 3 then 2 = 4C3 = 4

VPW; VPS; VWS; PWS

(ii) Two the same, third different: Choose the repeat in 4 ways, choose the one different 3 = 12

VVP; VVW; VVS; PPv; PPW; PPS; WWV; WWP; WWS; SSV; SSP; SSW.

(iii) All three the same. = 4

VVV; PPP; WWW; SSS

Total = 4 +12 + 4 = 20

Bob

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,526

Interestingly enough, the solution is also 6C3

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,395

It is also bobbym's age but I'm sure it is just a coincidence.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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I actually got the solution 6C3 from using a GF:

*Last edited by anonimnystefy (2013-01-10 11:35:06)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,771

Until infinitebrain gives a little more...

**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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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Hm?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,771

If order counts? If he wants different scoops or not.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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He does not. That is how you choose ice-cream scoops...

*Last edited by anonimnystefy (2013-01-10 08:31:38)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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He does not what?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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He does not want it without repetitions.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Then don't you think 64 is the answer as I said above?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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No, because you count vanilla, vanilla, strawberry combination 3 times! Order does not count.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,771

That is very good! So you agree with my answer of 20 in post #4 for when order does not count.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,526

Yes!

Look at post #8.

*Last edited by anonimnystefy (2013-01-10 10:23:24)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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I know, I saw it. It is very good.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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And very simple...

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,771

Hi;

Have you actually expanded your gf from post #8?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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Fixed it. I had my GFs mixed.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,771

Hi;

Looking good!

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,526

Thanks!

Here lies the reader who will never open this book. He is forever dead.

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**infinitebrain****Member**- Registered: 2008-07-01
- Posts: 153

Oh yes thanks guys for this! Thanks to you and a little more studying I figured it out!

The best thing about life is you don't know what to expect

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