Counting

 

   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 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.     

   _.