A mother duck lines her 13 ducklings up behind her. In how many ways can the ducklings line up

Discussion in 'Calculator Requests' started by math_celebrity, Apr 4, 2019.

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  1. math_celebrity

    math_celebrity Administrator Staff Member

    A mother duck lines her 13 ducklings up behind her. In how many ways can the ducklings line up?

    In position one, we can have any of the 13 ducks.
    In position two, we can have 12 ducks, since one has to occupy position one.
    We subtract 1 each time until we fill up all 13 positions.

    We have:
    13 * 12 * 11 * ... * 2 * 1

    Or, 13!. Typing 13! into our search engine, we get 6,227,020,800 ways the ducklings can line up behind the mother duck.
     

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