1. ## Combinations

I am trying to work out the number of combination's a particular problem has.

The problem:

Lets say there are 3 nodes. Each node is assigned a color, and there are three possible colors each node can be.

How many combinations are there?

Thanks

Calypso

2. Originally Posted by calypso
I am trying to work out the number of combination's a particular problem has.

The problem:

Lets say there are 3 nodes. Each node is assigned a color, and there are three possible colors each node can be.

How many combinations are there?

Thanks

Calypso
Hi Calypso,

Yes.

Suppose the nodes may be red, green or blue.
Then the combinations may be listed or you could draw a tree diagram

RRR
RRG
RRB

RGR
RGG
RGB

RBR
RBG
RBB

If the first node is Red, then there are 3(3) combinations.
We triple this to account for the first node being Green or Blue.

3. Great thanks for confirming the answer. Just have one further question if you dont mind..

Lets say now the three nodes are connected together by 3 bars. Each bar has a thickness and there are 10 possible thicknessess.

Going by the above logic the total number of combinations for bars is 3^10.

And the total combinations for nodes is 3^3

So does that mean that the total number of combinations including nodes and bars is

a ) (3^3) + (3^10)

b) (3^3) ^ (3^10)

c) (3^10) ^ (3^3)

Calypso

4. After thinking about the problem for a while I think the answer is more lilkely to be

d) (3^10) * (3^3)

Is this right?

5. Originally Posted by calypso
After thinking about the problem for a while I think the answer is more lilkely to be

d) (3^10) * (3^3)

Is this right?
That's almost it.

$\displaystyle 10^3(3^3)$

Taking any one arrangement of node colours...

The first bar can be any of 10 sizes,
2nd one can be any of 10 sizes,
3rd can be any of 10 sizes..

which is (10)(10)(10) arrangements of bar sizes with the 3 nodes connected
like a triangle, for any one colour combination.

6. Great, Thanks