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?

Question

Sawyer Woods

Mathematics

2 July, 23:09

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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Answers (1)

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Madilynn Wolf · Answer 1

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.