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If the different books of the same type are considered to be the same, so that different arrangements of the same type of book are not considered to be different variations in the answer, then to find the different arrangements of books simply multiply 3 X 4 to find the answer 12. If each book must be placed as a separate entity (each book is completely different and the books must all be arranged separately) then the answer is 7! (seven factorial), or 7 x 6 x 5 x 4 x 3 x 2 x 1. The answer in this case is 5040.

Examples:

Answer 12:

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Etc.

Answer 5040:

(Each number represents a different book. 4 are Algebra and 3 are Geometry, but all the books must be placed seperatly, so that makes no difference.)

1234567

7654321

7234561

7634512

Etc.

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Q: How many ways can you arrange 3 geometry books and 4 algebra books on a shelf?
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Related questions

How can you arrange 3 algebra books and 3 geometry books on a shelf so that no two books of the same type are next to each other?

Alternate them.


How can you arrange 3 algebra books and three geometry books on a shelf so that no two books of the same type are next to each other?

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5 books can be lined up on a shelf in (5 x 4 x 3 x 2 x 1) = 120 different sequences.


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