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Math Help - People Exiting an Elevator

  1. #1
    Member mybrohshi5's Avatar
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    People Exiting an Elevator

    8 people are in an elevator that goes up 6 floors. All 8 people exit the elevator by the 6th floor. The elevator operator is in the elevator watching them exit (the elevator operator does not count as one of the 8 people)

    How many ways can the people exit the elevator if they are all identical?

    This would just be \binom{6+8-1}{6-1} = \binom{13}{5}

    If there were 5 men and 3 women and the elevator operator could tell the men from women, how many ways could they exit the elevator?

    Men =  \binom{5+6-1}{6-1} = \binom{10}{5}

    Women =  \binom{3+6-1}{6-1} = \binom{8}{5}

    Thus, # of ways to exit =  \binom{10}{5} * \binom{8}{5}

    Now what if the elevator operator could distinguish each person (i.e. nobody is identical)

    Would this just be  6^8

    Thanks for any help!
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  2. #2
    MHF Contributor
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    Re: People Exiting an Elevator

    This sounds right to me.
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