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23 August, 04:38

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

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  1. 23 August, 05:08
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    So, the number of combinations is 57600.

    Step-by-step explanation:

    From Exercise we have

    5 different history textbooks

    4 different science textbooks

    For the place in the middle we have 4 books so the number of combinations for that place is 4.

    For the places at the end of the shelf I have 5 books, I need 2, so the number is a combination:

    2· / frac{5!}{ (5-2) !·2!}=2·10=20

    For the 6 places on the shelf I have 6 books so the number is a combination 6!=720

    So, the number of combinations is:

    4·20·720=57600.
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