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# The French tricolor flag is made up of three vertical stripes: red, white, and blue. Suppose you are given four different colors of fabric and asked to create a different flag using the same tricolor design. If no two adjacent stripes can be the same color, how many different combinations of color patterns are there?

Question #35911. Asked by RND. (Jul 05 03 3:12 PM)

Roget

24

 Jul 05 03, 3:22 PM
RND

Roget is correct - it would be cool if he would explain how he got that number...

 Jul 05 03, 3:26 PM
Roget

It is factorial 4, which is 4x3x2x1=24.

Another way is to think of the four colours, 1, 2, 3 and 4. If the left hand colour is 1 the possible combinations are 123, 124, 132, 134, 143 and 142. That's six possible combinations with 1 as the first colour. For each first colour there are 6 combinations, so 6x4=24.

 Jul 05 03, 3:32 PM

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