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Thread: What is probability English, PE, Math, science, history will be scheduled in order?

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    What is probability English, PE, Math, science, history will be scheduled in order?

    For next year's schedule of classes, math, English, history, science, and PE are each scheduled during the first five periods of the day. Your schedule is randomly selected by a computer. What is the probability that English, PE, Math, science, and history will be scheduled in that order? Round the nearest ten-thousandth.

    Please help. I cannot figure out whether to use a combination or permutation, or if that is even how you solve this question, Please provide the steps and explanation to the question.

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    Elite Member stapel's Avatar
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    Quote Originally Posted by sdd24 View Post
    For next year's schedule of classes, math, English, history, science, and PE are each scheduled during the first five periods of the day. Your schedule is randomly selected by a computer. What is the probability that English, PE, Math, science, and history will be scheduled in that order? Round the nearest ten-thousandth.

    Please help. I cannot figure out whether to use a combination or permutation, or if that is even how you solve this question, Please provide the steps and explanation to the question.
    For one of combinations and permutations, order matters. For the other, it does not. Since this exercise explicitly asks about a particular ordering, which do you think might be more useful?

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    Quote Originally Posted by stapel View Post
    For one of combinations and permutations, order matters. For the other, it does not. Since this exercise explicitly asks about a particular ordering, which do you think might be more useful?
    I used a permutation, since order matters. But I put it as 5P1, and got 5, then divided it by 25 because the total number of outcomes are 25. I got 0.2, is this correct?

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    Elite Member stapel's Avatar
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    Quote Originally Posted by sdd24 View Post
    I used a permutation, since order matters.
    Yes.

    Quote Originally Posted by sdd24 View Post
    But I put it as 5P1....
    Why? What is the "one of five" that you're picking? Aren't you picking all five classes, but in a particular order?

    Quote Originally Posted by sdd24 View Post
    ...and got 5, then divided it by 25 because the total number of outcomes are 25.
    Why? By what reasoning? (You may need to figure out what you're actually doing in the previous step, before you understand what to do in this step.)

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    There are five classes so the probability that English will be first, given that the classes are selected randomly with all classes equally likely is 1/5. There are then 4 classes left, all equally likely to be chosen as second class. What is the probability that PE will be chosen to be second? Continue like that. And use the fact that if A and B have probabilities p and q, then "A and B" has probability pq.

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