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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?

 Nov 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 not to have two yellows next to each other,    

the yellow color must occupy squares 1, 3, and 5.   

 

That leaves squares 2 and 4 to fill, and two colors    

to do it with. There are only four ways.   

 

Blue Blue     Red Red     Blue Red     Red Blue    

 

So, the answer is four ways.    

.    

 Nov 19, 2024

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