Math Is Fun Forum

infinitebrain

Member

Registered: 2008-07-01

Posts: 153

Combinatoric/Probability Problem

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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Combinatoric/Probability Problem

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.

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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.

cooljackiec

Member

Registered: 2012-12-13

Posts: 186

Re: Combinatoric/Probability Problem

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

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

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I see you have graph paper.
You must be plotting something

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Combinatoric/Probability Problem

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.

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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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Combinatoric/Probability Problem

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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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Combinatoric/Probability Problem

Interestingly enough, the solution is also 6C3

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Combinatoric/Probability Problem

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

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Combinatoric/Probability Problem

I actually got the solution 6C3 from using a GF:

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

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Combinatoric/Probability Problem

Until infinitebrain gives a little more...

---

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.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Combinatoric/Probability Problem

Hm?

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Combinatoric/Probability Problem

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

---

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.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Combinatoric/Probability Problem

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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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Combinatoric/Probability Problem

He does not what?

---

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.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Combinatoric/Probability Problem

He does not want it without repetitions.

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Combinatoric/Probability Problem

Then don't you think 64 is the answer as I said above?

---

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.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Combinatoric/Probability Problem

No, because you count vanilla, vanilla, strawberry combination 3 times! Order does not count.

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Combinatoric/Probability Problem

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

---

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.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Combinatoric/Probability Problem

Yes!

Look at post #8.

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

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Combinatoric/Probability Problem

I know, I saw it. It is very good.

---

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.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Combinatoric/Probability Problem

And very simple...

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Combinatoric/Probability Problem

Hi;

Have you actually expanded your gf from post #8?

---

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.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Combinatoric/Probability Problem

Fixed it. I had my GFs mixed.

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Combinatoric/Probability Problem

Hi;

Looking good!

---

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.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Combinatoric/Probability Problem

Thanks!

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

infinitebrain

Member

Registered: 2008-07-01

Posts: 153

Re: Combinatoric/Probability Problem

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

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