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
OOPS I FORGOT TO ADD THIS
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
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!
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! :)