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?

LiIIiam0216 May 6, 2024

#1**0 **

In order not to have two yellows next to each other,

the three yellows 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**.

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Bosco May 6, 2024

#3**0 **

Total ways: 35=24335=243. Ways with <3 yellow: 1+2(51)=211+2(15)=21. So, 243−21=222243−21=222 ways with at least three yellow squares.

sunflower36002 May 7, 2024