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Math Help - conference problem...

  1. #1
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    conference problem...

    A conference attended by 200 delegates is held in a hall. The hall has 7 doors, marked A,B,C,.....,G. At each door, an entry book is kept and the delegates entering through that door sign it in the order in which they enter. If each delegate is free to enter any time and through any door he likes, how many different sets of seven lists would arise in all ? (Assume that every person signs only at his first entry.)



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  2. #2
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    Hint -
    There are two ways list will differ
    1. number of people entering from each door
    2. Order of people

    Can you make an attempt now?
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  3. #3
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    nopes.
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  4. #4
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    ok. Let us relax the condition that the delegates are different. So treat them as 200 identical balls to be dropped in 7 different urns (the doors). How many ways you can do that?
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  5. #5
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    Do I need to apply pigeon hole principle ?
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  6. #6
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    No
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