Permutations: Arranging Red, Green & Gray Books on a Shelf

[Government$]

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!

 

[tiny-tim]

Hi Government$!

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!

 

[pbuk]

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...".