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frx Group Title

A collection of books has 5 books on mathematics, 7 books on physics and 6 books on chemistry. In how many ways can you combine the collection on a shelf if you want the same subject to stand together? The combinations within each subject should be, 5!, 7! and 6!, right? But how do i calculate the combinations so that they stand together?

  • one year ago
  • one year ago

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  1. satellite73 Group Title
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    there are \(3!=6\) ways to arrange the three subjects

    • one year ago
  2. satellite73 Group Title
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    so multiply all that together and then multiply by 6

    • one year ago
  3. frx Group Title
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    Multiply which together? 5!6!7! ?

    • one year ago
  4. satellite73 Group Title
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    yup

    • one year ago
  5. frx Group Title
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    Who did you choose what to divide with?

    • one year ago
  6. frx Group Title
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    Permutations like? \[\frac{ 5!6!7! }{ (5!6!7!-?) }\]

    • one year ago
  7. satellite73 Group Title
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    hold on

    • one year ago
  8. satellite73 Group Title
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    you are taking all the books right? don't get married to these formulas the number of ways to arrange items is 5! by the counting principle. similarly for 6 items and 7 items this is not asking you how many ways you can arrange 4 out of 10 for example

    • one year ago
  9. satellite73 Group Title
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    \(5!\) ways for math books, by the counting principle \(6!\) ways for the chemistry books by the counting principle and \(7!\) ways for the physics books, again by the counting principle there if you had them arranged as {math, physics, chemistry} then again by the counting principle there would be \(5!6!7!\) ways to arrange the books, but there are \(3!=6\) arrangments of the subjects, so you again need to multiply by 6 i.e. \(3!5!6!7!\)

    • one year ago
  10. frx Group Title
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    Oh I get it! Thank you so much! :D

    • one year ago
  11. satellite73 Group Title
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    yw

    • one year ago
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