Question 339880: each of the six squares shown in the figure is to be filled with any one of the ten possible colors. how many ways are there of coloring the strip shown in the figure so that no two adjacent squares have the same color?
their is a purple box, a yellow box, a red box , a green box, a blue box and and an orange box lined up next to each other.
Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website!
Fill the 1st square any of the 10 ways.
That's 10 ways to color the 1st square.
For every one of those 10 ways to color the 1st square, there
are 9 ways to color the 2nd square, that is, with any of the
9 colors different from the color in the 1st square.
That's 10*9 ways to color the first 2 squares.
For every one of those 10*9 ways to color the 1st 2 squares, there
are 9 ways to color the 3rd square, that is, with any of the
9 colors different from the color in the 2nd square.
That's 10*9*9 ways to color the first 3 squares.
For every one of those 10*9*9 ways to color the 1st 3 squares, there
are 9 ways to color the 4th square, that is, with any of the
9 colors different from the color in the 3rd square.
That's 10*9*9*9 ways to color the first 4 squares.
For every one of those 10*9*9*9 ways to color the 1st 4 squares, there
are 9 ways to color the 5th square, that is, with any of the
9 colors different from the color in the 4th square.
That's 10*9*9*9*9 ways to color the first 5 squares.
For every one of those 10*9*9*9*9 ways to color the 1st 5 squares, there
are 9 ways to color the 6th square, that is, with any of the
9 colors different from the color in the 5th square.
That's 10*9*9*9*9*9 ways to color the first 6 squares.
That's all the squares, so the answer is
10*95 = 590490 ways.
Edwin
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