1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Probability arranging books

  1. Nov 19, 2012 #1
    1. The problem statement, all variables and given/known data
    there are 7 different french books and 7 different Spanish books, how many ways are there to arrange them on a shelf
    a. books of the same language must be group together, French on left and Spanish on Right?
    b. French and Spanish books must alternate in the grouping, beginning with a French book?

    I tried doing 7!x7! for both of them but i don't think i am right?

    I have no idea how to approach this
     
  2. jcsd
  3. Nov 19, 2012 #2

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Sounds right to me.
     
  4. Nov 22, 2012 #3
    for the first one 7!x7! seems right, but for the 2nd one I think (not sure...!!!) it's :

    7C1X7C1 X 6C1X6C1 X 5C1X5C1 X 4C1X4C1 X 3C1X3C1 X 2C1X2C1 X 1C1X1C1
     
  5. Nov 22, 2012 #4

    CAF123

    User Avatar
    Gold Member

    I think an argument could go: there are 14 choices for the first book, (French or Spanish). There are then 7 choices for the next book (If first was French, this one must be Spanish), then 6 choices for next, (has to be French), then 6 choices for next (has to be Spanish)....and so on. In this Q, the French book is first so what you wrote is correct.
     
    Last edited: Nov 22, 2012
  6. Nov 22, 2012 #5

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Another argument: for each arrangement of the French books, leave a space between successive books and fill those spaces with the Spanish books, one book per space.

    RGV
     
    Last edited: Nov 22, 2012
  7. Nov 22, 2012 #6

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    How is that different from 7!x7!?
    The two obviously have the same answer. Either way, there is a fixed set of 7 positions that can be taken by the French books, and another fixed set of 7 that can be taken by the Spanish, independently.
     
  8. Nov 22, 2012 #7

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    It's not different; it's just another argument that the OP may, or may not, prefer.

    RGV
     
  9. Nov 22, 2012 #8

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    I was replying to MadAtom, who wrote:
    the first one 7!x7! seems right, but for the 2nd one I think (not sure...!!!) it's :​

    Seems to me MadAtom implied 7!x7! was wrong for the second question.
     
  10. Nov 23, 2012 #9
    I thought so, but the result is the same... sorry.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Probability arranging books
  1. Arranging Formulas (Replies: 4)

Loading...