Linear Permutation of Grouped Things

Question

I can not search this over the internet so I thought some of you guys can help me out. The question goes like this.

There are 15 books. Of these are 5 Mathematics, 7 Physics, and 3 books on Chemistry. In how many ways can they be arranged in a shelf if the three subjects are to be grouped together?

P.S. I tried the using the permutation formula involving identical elements. But it's not arriving to the right answer in my book. Thanks in advance.

Answer 1

It doesn't seem like the permutation formula involving identical elements should apply here -- after all, the different Mathematics books are not identical. None of the fifteen books are identical.

I think the best way to think about this question is as follows: since each group must remain together, first choose the order of the groups, then choose the order within each group.

Answer 2

The number of ways of each books can be arranged is: $5!\times7!\times3!$ = $3628800$. The number of ways the subjects (group) can be arranged is: $3! = 6$.

Multiply both results = $21772800$.