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    ernieis3's Avatar
    ernieis3 Posts: 2, Reputation: 1
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    #1

    Apr 18, 2011, 04:42 PM
    50 letters
    A secretary addresses 50 different letters and envelopes to 50 different people, but the letters are randomly mixed before being put into envelopes. What is the probability that at least one letter gets into the correct envelope?
    galactus's Avatar
    galactus Posts: 2,271, Reputation: 282
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    #2

    Apr 19, 2011, 10:22 AM

    This is known as a derangement.

    The probability that no letter ends up in its envelope is



    This is the series for 1/e. So, for large N, the probability approaches around 37%.

    So, for the probability that at least one gets in its envelope would be 1 minus the above.



    About 63.2%
    jcaron2's Avatar
    jcaron2 Posts: 986, Reputation: 204
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    #3

    Apr 19, 2011, 07:49 PM
    Comment on galactus's post
    Cool! I'd never heard of derangement before (at least not this particular definition - lol!).
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