1. R
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    In a lecture of 100 students, the teacher pre-selects 8 books { A,B,C,D,E,F,G,H }. Each of the students is instructed to read 6 out of the 8 pre-selected books by the end of the term. At a minimum; how many times is the set of books {A,C,E,F,G,H} read?
  2. Standard memberBigDogg
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    16 Mar '21 16:03
    @joe-shmo said
    In a lecture of 100 students, the teacher pre-selects 8 books { A,B,C,D,E,F,G,H }. Each of the students is instructed to read 6 out of the 8 pre-selected books by the end of the term. At a minimum; how many times is the set of books {A,C,E,F,G,H} read?
    We could get very unlucky.

    If all 100 of them happen to pick C through H, then book A is never read, and the answer is 0.
  3. R
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    16 Mar '21 16:103 edits
    @bigdoggproblem said
    We could get very unlucky.

    If all 100 of them happen to pick C through H, then book A is never read, and the answer is 0.
    You are correct! Not the question I actually wanted the answer to, but that is my fault ( tweaking problems has its downfalls ). I'm going to try and reformulate and ask another question.
  4. R
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    16 Mar '21 16:55
    A better question...I hope ( should be, since I'm reposting it as I experienced it).

    Students in a lecture are assigned to read 6 of 8 pre selected books from the instructor by the end of the term. At the end of the term, the instructor found that any selection of six books was read at most 4 times in the class. What is the maximum number of students that could be attending the class?
  5. Subscribervenda
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    16 Mar '21 20:00
    @joe-shmo said
    A better question...I hope ( should be, since I'm reposting it as I experienced it).

    Students in a lecture are assigned to read 6 of 8 pre selected books from the instructor by the end of the term. At the end of the term, the instructor found that any selection of six books was read at most 4 times in the class. What is the maximum number of students that could be attending the class?
    6 out of 8- 28 combinations
    4*28 -112 students
  6. R
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    16 Mar '21 20:07
    @venda said
    6 out of 8- 28 combinations
    4*28 -112 students
    Correct Venda!
  7. R
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    17 Mar '21 02:08
    In a class of 100 students, what is the probability at least 4 students read books { A,B,C,E,G,H }?
  8. R
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    17 Mar '21 15:381 edit
    As a precursor to the last question:

    In a class of 100 students what is the probability that exactly "n" people read the set { A,B,C,E,G,H}?
  9. Subscribervenda
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    17 Mar '21 19:37
    @joe-shmo said
    In a class of 100 students, what is the probability at least 4 students read books { A,B,C,E,G,H }?
    no of books 6 out of 8 =28
    no of students = 100
    no of books read =4 out of 100 students
    big numbers but the probability comes out at .0007.
    Think I might have gone wrong somewhere!
  10. R
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    17 Mar '21 19:50
    @venda said
    no of books 6 out of 8 =28
    no of students = 100
    no of books read =4 out of 100 students
    big numbers but the probability comes out at .0007.
    Think I might have gone wrong somewhere!
    I can't figure out your calculation, but its not correct. Perhaps try to answer the next question first ( sorry about the flipped chronology ) its crucial to answering this question.

    What is the probability is that no one reads the set { A,B,C,E,G,H }?
  11. Subscribervenda
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    17 Mar '21 22:24
    @joe-shmo said
    I can't figure out your calculation, but its not correct. Perhaps try to answer the next question first ( sorry about the flipped chronology ) its crucial to answering this question.

    What is the probability is that no one reads the set { A,B,C,E,G,H }?
    Bit late now.
    I'll have another think tomorrow.
    If anyone else wants to answer,I don't mind
  12. R
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    18 Mar '21 00:57
    @venda said
    Bit late now.
    I'll have another think tomorrow.
    If anyone else wants to answer,I don't mind
    No pressure. I'm just leaving some bread crumbs!
  13. Standard memberBigDogg
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    18 Mar '21 01:06
    @joe-shmo said
    I can't figure out your calculation, but its not correct. Perhaps try to answer the next question first ( sorry about the flipped chronology ) its crucial to answering this question.

    What is the probability is that no one reads the set { A,B,C,E,G,H }?
    I got 2.6%, but I have trouble believing that answer.
  14. R
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    18 Mar '21 01:253 edits
    @bigdoggproblem said
    I got 2.6%, but I have trouble believing that answer.
    That is correct. The probability of of no one reading that set is:

    P( n = 0 ) = ( 27/ 28 )^100 ≈ 2.6%

    so the ball is rolling.

    The next forward step would be to answer:

    In a class of 100 students what is the probability that exactly "n" people read the set { A,B,C,E,G,H}?
  15. Subscribervenda
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    18 Mar '21 09:011 edit
    @joe-shmo said
    That is correct. The probability of of no one reading that set is:

    P( n = 0 ) = ( 27/ 28 )^100 ≈ 2.6%

    so the ball is rolling.

    The next forward step would be to answer:

    In a class of 100 students what is the probability that exactly "n" people read the set { A,B,C,E,G,H}?
    Sorry Joe,I seem to have lost this.
    I don't understand the equation.
    Are you saying 27/28 to the power 100?
    Also I don't see where 27 divided by 28 comes from.
    Perhaps it's the way the question is posed.
    Are you saying 1 book out of the set{abc etc) or all the books in set{abcetc)?
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