Combinatorics is a cool subject because it takes really simple principles like "n choose k," Pascal's triangle, etc and is able to ascertain quite a lot of new information.
I like the mixing of tools in math to solve more complicated and not at all intuitive problems, such as the proof that binomial coefficients are integers.
Why are induction proofs considered inelegant? They are powerful.
I don't really know what else to say about this chapter...
-Batman
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