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In a row of five squares, each square is to be colored either red, yellow, or blue, so that no two consecutive squares have the same color. How many ways are there to color the five squares, if there must be at least three yellow squares?

 Mar 19, 2024
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In a row of five squares, each square is to be colored either red, yellow, or blue, so that no two consecutive squares have the same color. How many ways are there to color the five squares, if there must be at least three yellow squares?  

 

In order to avoid having two yellows next to each other,  

the three yellows must occupy squares 1, 3, and 5. 

 

That leaves squares 2 and 4 to account for, and two   

colors do it with. There are only four ways. 

 

Red Red     Blue Blue     Red Blue     Blue Red   

 

So, the answer is four ways.  

.

 Mar 19, 2024

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