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!
Best Answer
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 ...