Arranging red, green, and gray books with same-color grouping

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Government$
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Homework Statement



1.) 4 of the books have red covers, 3 have green covers, and another 2 have gray covers. In how many ways can the books be arranged on a shelf if books of the same color must be arranged together?


The Attempt at a Solution



1) I think that the answer here is 3!

But here is the answer from my book (4!3!2!)3!
 
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Discussion

Hi Government$! :smile:
Government$ said:
1.) 4 of the books have red covers, 3 have green covers, and another 2 have gray covers. In how many ways can the books be arranged on a shelf if books of the same color must be arranged together?
…
1) I think that the answer here is 3!

That's correct only if books of the same colour are stuck together! :wink:
 
If the answer they are looking for is 4!3!2!3! it would have been less ambiguous to pose the question as "There are 9 different books. 4 of the books have red covers...".