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In how many ways can we select two books from different subjects among five distinct computer science books, three distinct mathematics books, and two distinct art books?

I was able to answer the above question by creating a tree diagram, however, I want to be able to understand the results using permutation/combination theory. Is anyone willing to explain? This is what I got after conducting the tree diagram: CM or CA or AM 15 + 10 + 6 = 31 ways. I don't want to take the long route in answering questions like this in the future.

Thanks for all your help!

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  • $\begingroup$ See here: math.stackexchange.com/questions/87629/… Might help $\endgroup$ – Joseph Eck Jun 19 '18 at 19:51
  • $\begingroup$ If each individual book is different from each other, such as "Algebra II" and "Calculus", then it's simply $P_{2}^{10}$ $\endgroup$ – Joseph Eck Jun 19 '18 at 20:01
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Well, your basic method of splitting this into 3 cases is correct:

Case 1: Comp Sci book + Math book (CM): $5$ choices for the C book, and $3$ choics for the Math book gives $5 \cdot 3 = 15$ options

Similarly, Comp Sci and Art (CA) gives $5 \cdot 2=10$ options, and Math plus Art (MA) gives $3 \cdot 2 = 6$ options.

Really not sure how you could do this more efficiently ...

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