Aery is coloring the three segments of a pinwheel with rainbow colors (red, orange, yellow, green, blue, indigo, or purple). By the way the pinwheel only has 3 segments so she colors all of them

 Aug 9, 2022


I made a list of possible colors and this is how it looks so far

Red Oragne YelloW
Red oragne green

red orange blue

red orange indigo

red orange purple

I made this list because i am more of a visual learner but any help would be appreciated

 Aug 9, 2022

Don't list them all out. That's an unwritten rule for solving a counting math problem. 


For the first segment, you have 7 colors to choose from.

For the second and third segment, you also have 7 choices for both of them. Therefore, there would be 7^3 = 343 ways to color all of them. 


Yikes, if you listed them all out, you would have 343 ways! 

 Aug 9, 2022

I'm also a visual learner, so here is what I think should help you visualize it.


These are the three spaces -->       _ _ _

_  _  _

R  R  R

O  O  O

Y  Y  Y

G  G  G

B  B  B

I  I  I

P  P  P


These are the seven choices for each space


So lets cut it down to 2 spaces to make it easier

Each choice of the first space has 7 choices for the next space

the same for each number going down the list

R has 7 choices for the next space, O has 7 choices for the next space, and so on

=> This makes 7 + 7 + 7 + 7 + 7 + 7 + 7 = 7 * 7 = 7^2

 So if you repeat this method for 3 spaces, you get 7^3 which equal 343 ways.


Hope this helps! :)

 Aug 9, 2022
edited by calvinbun  Aug 9, 2022

So sorry I forgot to add this part. Combinations count as one if they can be rotated to look like each other. Ex: Red Orange Yellow would be the same as Orange Red Yellow

 Aug 9, 2022

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