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There are $5$ chemistry and $4$ physics books. How many ways can these books be arranged in a manner that physics and chemistry books will be among themselves?

By visualizing what question wants me to do, I drew a diagram as illustrated below. Recall $C$ chemistry book, $P$ physics book.

$$C_{1}C_{2}C_{3}C_{4}C_{5}P_{1}P_{2}P_{3}P_{4}$$

It seems to be enough to solve the question. However, how do I rewrite it mathematically now?

Mark
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  • Could I ask why my question has been downvoted? – Mark Oct 06 '18 at 14:28
  • Considering all the books different, the answer is 9! – ab123 Oct 06 '18 at 14:36
  • Question is not quite clear. As ab123 says, for 9 different books there are 9! arrangements. I suspect though that the question only wants you to differentiate between Chemistry and Physics, so more like CCCCCPPPP being one arrangement. – Paul Oct 06 '18 at 14:43
  • I didn't mean that. The question wants me to determine it in a manner that Physics and Chemistry books will be among themselves. For instance, you cannot do CCCPCPPPC – Mark Oct 06 '18 at 16:00
  • $2\cdot 4!\cdot 5! =5760$ – Fabio Lucchini Oct 07 '18 at 12:51

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