Applied Combinatorics by Alan Tucker is a good one. It's short, not hard to follow, a lot of problems to work through, and it's split into two sections: graph theory in section 1, and combinatorics (generating …

In fact,I once tried to define combinatorics in one sentence on Math Overflow this way and was vilified for omitting infinite combinatorics. I personally don't consider this kind of mathematics to be …

Is there a comprehensive resource listing binomial identities? I am more interested in combinatorial proofs of such identities, but even a list without proofs will do.

Jan 11, 2016 · Combinatorics is a wide branch in Math, and a proof based on Combinatorial arguments can use many various tools, such as Bijection, Double Counting, Block Walking, et cetera, so a …

Oct 17, 2018 · Comically badly worded question - particularly amusing is the phrase 'each card displays one positive integer without repetition from this set' :) it's almost like the output of a bot fed …

Jun 28, 2017 · \mathchoice((((n k\mathchoice)))) \mathchoice ((((n k \mathchoice)))) - n choose k - how many different ways there are to pick k k items from a set of n n elements. The explanation starts …

Aug 24, 2013 · If you want a slightly more detailed explanation and exercises I recommend the book Introduction to Combinatorics published by the United Kingdom Mathematics Trust (UKMT) available …

Mar 18, 2020 · Imagine we want to put $7$ stars in $3$ bins. We can use a visual representation to show how we organise them: $$★ ★ ★ ★ | ★ | ★ ★$$ The bars split the different bins. So, according …

I get that it is including all of the duplicates, too. And to get rid of them we use the combinations formula:

Dec 6, 2021 · Can someone please explain what double counting is? I have no idea what it is, and Google search yields results that are too complicated for me to understand at this point in time. If …