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Math Help - problem with sets and counting again

  1. #1
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    problem with sets and counting again

    I am having a lot of problems with this problem, I went to a tutor and showed me what to do, but I still get it wrong. Im on the verge of failing, so i want to get the best possible grades on my homework. Please help me with this problem:

    If a die is rolled 40 times, there are 640 different sequences possible. What fraction of these sequences have exactly 8 numbers less than or equal to 3? (Round your answer to the nearest 0.0001.)
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  2. #2
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    Quote Originally Posted by Flamed02 View Post
    If a die is rolled 40 times, there are 640 different sequences possible. What fraction of these sequences have exactly 8 numbers less than or equal to 3? (Round your answer to the nearest 0.0001.)
    First a correction: there are 6^{40} different sequences possible.
    On any toss of the die there is a probability of 0.5 that the die shows 3 or less.
    There are {40 \choose 8}, 40 places choosing 8, to have success.
    So the answer: {40 \choose 8}(0.5)^{40}
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  3. #3
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    thank you, my answer was 6.994440355 E-5 What does the E-5 mean?
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