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# Thread: permutation problem: how many ways to color a flag with 5 horizontal strip?

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## permutation problem: how many ways to color a flag with 5 horizontal strip?

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How to solve this problem?

A flag contains 5 horizontal strips. In how different ways can the flag be painted using 4 different colors such that one color is painted per strip and no two adjacent strips have the same color?

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The answer is: 4*3pow4.

The first strip can be painted in 4 ways. After that next can be painted in 3 ways as one paint is used in 1st strip. Same logic for painting rest of strips.
Total no. of ways = 4*3pow4.

Let me know if this helps.

Regards
Abhijit.

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This problem appeared in IIM-CAT 2004 for admission into the Indian Institutes of Management

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