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In a class, 18 students like to play chess, 23 like to play soccer, 21 like biking, and 17 like jogging. The number of those who like to play both chess and soccer is 9. We also know that 7 students like chess and biking, 6 students like chess and jogging, 12 like soccer and biking, 9 like soccer and jogging, and finally 12 students like biking and jogging. There are 4 students who like chess, soccer, and biking, 3 who like chess, soccer, and jogging, 5 who like chess, biking, and jogging, and 7 who like soccer, biking, and jogging. Finally, there are 3 students who like all four activities. In addition, we know that every student likes at least one of these activities. How many students are there in the class?

I know this is a case of using the inclusion-exclusion principle, but I'm a little overwhelmed, given that there are 4 sets. Can someone please explain this to me? Thanks!

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    This is absolutely not something to be tagged under set-theory. At most it might fit under elementary-set-theory. I would still protest, as this is a question about discrete mathematics more than it is about set theory.2011-05-03
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    Oh that was my mistake. I started filling in a tag about sets and clicked the wrong one. Sorry!2011-05-03
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    It's fine, just try not to be so harsh on the Save Edits the next time. :-)2011-05-03

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