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Thread: Room Assignments

  1. #1
    Jan 2007

    Room Assignments

    Suppose 4 people were randomly assigned into 9 rooms (numbering 1 to 9). Each person can be asigned equally likely and each room can hold more than one person.

    a) What is the probability that from rooms 1 to 4 there are exactly one person each?

    b) What is the probability that there are exactly 3 people in room 8?
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  2. #2
    MHF Contributor

    Aug 2006
    Taking the problem at face value, it is possible to assign all four to the same room, then there are $\displaystyle 9^4$ ways to do it.

    If part a means the only rooms 1,2,3,&4 have a person in them then there are $\displaystyle 4 !$ ways to do that.

    There are $\displaystyle 4 \choose 3$ to choose three to put in room eight. There are then 8 ways to assign the other person.
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