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4 August, 20:00

I have $5$ different physics textbooks and $4$ different chemistry textbooks. In how many ways can I place the $9$ textbooks on a bookshelf, in a row, if there must be a chemistry textbook in the middle, and there must be a physics textbook at each end

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  1. 4 August, 21:34
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    Answer: 57600

    Explanation:

    Given the following;

    5 different physics textbooks

    4 different chemistry textbooks

    There are 9 different positions for arranging the textbooks on a shelf.

    If there must be a physics textbook at both ends;

    Number of physics textbooks = 5

    Both ends = 2 different positions

    Mathematically,

    5P2 = 5! : (5-2) !

    5! : 3!2! = (5*4)

    5P2 = 20 ways

    If a chemistry textbook must be in the middle;

    Number of chemistry textbooks = 4

    Middle = 1 position

    Mathematically,

    4P1 = 4! : (4-1) !

    4P1 = 4! : 3!

    4P1 = 4 ways

    3 positions have been calculated,

    The 6 positions left = 6!

    6! = 720ways

    Therefore,

    6! * 5P2 * 4P1 = 720 * 20 * 4 = 57600
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