A bookshelf contains 3 Russian novels, 4 German novels and 5 Spanish novels. All the Spanish novels must be together and no constraint on the order of the others. How many ways can you arrange these books?
1 Answer
Explanation:
Spanish Novels - internal ordering
The novels must be kept together and so we'll have them be a block of books on the shelf.
How many ways can we order the Spanish novels?
Spanish Novels - placement
We now have a block of 5 books to place on the shelf. There are 12 books in total, and so 12 spots for books. The block of Spanish novels can be in spots 1 - 5, 2 - 6, 3 - 7, 4 - 8, 5 - 9, 6 - 10, 7 - 11, 8 - 12, or 8 spots in total.
The other novels
We can place the 7 remaining novels in the remaining 7 spots in
All together
And so all told, we can arrange the books:
(If this seems like a lot, keep in mind that without the constraint on the Spanish novels, we could have arranged the books in