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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?

  • 2 years ago
  • 2 years ago

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

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

    • 2 years ago
  3. frx Group Title
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    Multiply which together? 5!6!7! ?

    • 2 years ago
  4. satellite73 Group Title
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    yup

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

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

    • 2 years ago
  7. satellite73 Group Title
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    hold on

    • 2 years 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

    • 2 years 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. \(3!5!6!7!\)

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

    • 2 years ago
  11. satellite73 Group Title
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    yw

    • 2 years ago
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