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June 18th, 2012, 02:05 PM   #1
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Ordered distribution of distinct objects into distinct conta

Hi!

The other day I found a problem which asked me to find the number of ways to place 13 flags on 7 flagpoles, where a)The order of the flags on a flagpole is not relevant b)The order of the flags on a flagpole is relevant.

Obviously, the answer to part a) is . However, in part b), we are facing the situation of an ordered distribution of distinct objects into distinct containers. How would one solve this?

Thanks in advance!
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June 18th, 2012, 03:37 PM   #2
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Re: Ordered distribution of distinct objects into distinct c

If you label your flags A thru M, and 7 flag poles, each as P.

And consider sequences of those letters, then the second part of your question is equivalent to how many sequences are there consisting of those 20 letters where each sequence starts with a P.

We consider, for example, any flags between the 3rd and 4th Ps to be on the 3rd flag pole, in the same order as in the sequence, etc.

I.e how many arrangements are there of the remaining 19 items where 6 are the same.
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June 22nd, 2012, 05:59 PM   #3
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Re: Ordered distribution of distinct objects into distinct c

Thank you. I have solved the problem.
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