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Subject: "Permutation Expression"     Previous Topic | Next Topic
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creator83
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Oct-25-00, 11:06 PM (EST)
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"Permutation Expression"
 
   How do I prove: how many permutations of 0,1,...,n-1 that leave the ORDER of elements 0,1,...,k-1 undisturbed, k is less or equal to n?


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alexb
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Oct-26-00, 12:56 PM (EST)
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1. "RE: Permutation Expression"
In response to message #0
 
   Think of it the following way. Elements 0, 1, ..., k-1 are fixed. Draw the number line and vertical bars at k points which should be denoted 0, 1, ..., k-1. This bars divide the line into k+1 buckets. The question is now, in how many ways can you put the remaining n-k elements into those k+1 buckets? This is the same as askng, in how many ways n-k buckets can be selected out of k+1 with repitions allowed?

Can you pick up from here?


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