Verified answer

Given that there are 12 books consisting of 5 dictionaries, 3 mathematics books, and 4 science books such that books of the same kind are indistinguishable, then number of distinguishable permutations will be:

Another way to think about this problem is to choose five of the twelve spaces in which to place the dictionaries - since the order of selection is not important, there are ways to do this. Then, from the remaining 7 spaces available, we need to choose three of them in which to place the mathematics books. There are ways to do that. The four science books are then placed in the remaining four spaces.

The result of this process is that there are ways to choose the places for the dictionaries and ways to choose the places for the mathematics books, which results in:

This results in the same answer as when we approached the problem as a distinguishable permutation.