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Math Help - Probability - ordering

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    Probability - ordering

    Each of 6 historical events occurred in a different year. You are asked to arrange the 6 events in ascending order by the years they occurred. You know the earliest and the latest. You randomly order the other events. What is the probability that you order the 6 events correctly?
    I think my instructor said the correct answer was 1/24 but I'm not sure how to solve..
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by donnagirl View Post
    Each of 6 historical events occurred in a different year. You are asked to arrange the 6 events in ascending order by the years they occurred. You know the earliest and the latest. You randomly order the other events. What is the probability that you order the 6 events correctly?
    I think my instructor said the correct answer was 1/24 but I'm not sure how to solve..
    this is a permutation question. the number of possible arrangments you have for the remaining 4 events, are 4!  = 24. only one of these arrangements are correct. thus the probability of you choosing that arrangement is \frac 1{24}

    one way to think of the permutation is to say, you have 4 choices for the event in the second position, for each of those, you have three choices for the third position, for each of those, two choices for the fourth position and one choice for the 5th. in all, that is 4*3*2*1 = 4! choices
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