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anonymous

  • 5 years ago

Find the number of ways in which 3 different history books, 4 different English books, and 5 different Algebra books can be arranged on a shelf so that the books in a given subject are grouped together.

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  1. anonymous
    • 5 years ago
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    3P3 x 4P4 x 5P5 x 6 = 103,680 since there are 6 ways of arranging subjects ?

  2. anonymous
    • 5 years ago
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    why times 6

  3. anonymous
    • 5 years ago
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    like why are there 6 ways of arranging them.. how did you figure that out?

  4. anonymous
    • 5 years ago
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    ok, ill have a go at this one , but its been like 2years since I last really did solid study of combinatorics lol

  5. anonymous
    • 5 years ago
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    lolololol

  6. anonymous
    • 5 years ago
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    so it should be = 3! x 4! x 5! x 3!

  7. anonymous
    • 5 years ago
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    check if thats the answer, before I try to explain it

  8. anonymous
    • 5 years ago
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    right

  9. anonymous
    • 5 years ago
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    I dont like doing the whole nPr notation, its lazy

  10. anonymous
    • 5 years ago
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    i understand how to do it, all i dont understand is why there is a second 3 factorial added to the equation

  11. anonymous
    • 5 years ago
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    you consider them as seperate groups

  12. anonymous
    • 5 years ago
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    you group the subjects together

  13. anonymous
    • 5 years ago
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    there are n! ways of arranging n objects in a group

  14. anonymous
    • 5 years ago
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    and then there are 3! ways of arranging your groups in a line

  15. anonymous
    • 5 years ago
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    there are 6 ways of arranging the subjects as if you have a, b and c , you can arrange them as {a,b,c},{a,c,b},{b,a,c},{b,c,a},{c,a,b}{c,b,a}

  16. anonymous
    • 5 years ago
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    it takes a little getting used to , I wasnt quite sure about it the first I saw it either

  17. anonymous
    • 5 years ago
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    my teacher sucks, so I had no clue

  18. anonymous
    • 5 years ago
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    it gets even more complex if you were to say arrange them in a circular loop

  19. anonymous
    • 5 years ago
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    or if you only arrange a subset of them in a circle, thats about as tricky as they come !v

  20. anonymous
    • 5 years ago
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    I should have done a maths degree instead of engineering lol :|

  21. anonymous
    • 5 years ago
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    haha you should have!!! you are very very good at math!

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