question archive In a string, distance between two symbols is the number of symbols between them plus one

In a string, distance between two symbols is the number of symbols between them plus one

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In a string, distance between two symbols is the number of symbols between them plus one. For example, in a string xyyx, y is at distance 1 from another y, and x is at distance 3 from another x. Find the number of strings of length n using at most k distinct symbols, such that the minimal distance between any two identical symbols is k. 

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Answer:

Require number of strings = { kPn , if n ≤ k ; k!, if n < k }

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