I don\'t think the solution to this questions is correct. The problem is: The ne

Question

I don't think the solution to this questions is correct. The problem is: The new book shelf at a library contains two novels, six biographies, and four how-to books. in how many ways can the books be arranged on the shelf if the books for each category are placed together? The provided answer for this question says only 6 ways. Only looking at the sets, there are six ways possible; however, can't the books within each category also be arranged in multiple ways? Do you add or multiply the number of possible combinations for each together? Do you multiply of the number of combinations for each subset times the 6 ways the whole sets (each category) can be arranged?

Explanation / Answer

You're right about the 6 ways being only about the ways the 3categories can be ordered. For each such ordering of thecategories on the shelf, one can order the novels in 2 ways, thebiographies in 6! ways, and the how-to books in 4! ways, whichgives 6*2*6!*4! = 207360 ways. Are you sure there isn't some underlying assumption that the booksin each category are somehow ordered?

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