Freight labeling riddle


At the local Puzzlefry Internet dispatch center, the packing department was getting ready for the weekend.

However, it was late in the day and the final five packages were ready to be labelled.

Unfortunately, John dropped the labels to the packages and then had no idea which label belonged to which packet.

What is the probability that John managed to correctly label exactly four of the five packages?

SherlockHolmes Expert Asked on 6th February 2018 in Math Puzzles.
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  • 2 Answer(s)

    Assumption: The dispatch centre does NOT prepare labels in excess of packages, neither do they leave any package unlabeled. (i.e., if there are ‘P’ packages and ‘L’ labels, P =L.)

    The probability of the scenario specified in the puzzle happening is ZERO.

    Explanation: Since there were only FIVE Packages left to be labelled, if John managed to label FOUR of them correctly, it means that the fifth package was also labelled correctly, because there are no excess labels prepared so that the fifth package could get mislabeled. Thus, the result will be that ALL FIVE packages are correctly labelled. Hence, it is impossible to have “exactly four of the five packages” labelled correctly.

    Viji_Pinarayi Expert Answered on 15th February 2018.
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    probability exactly 4 packages getting labeled correctly is = 0
    ( but at least 4 packages getting labeled correctly is : 1/5! = 1/120 = 0.0083333 )

    Chathura Scholar Answered on 23rd February 2018.
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