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 …

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 …

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 …

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.

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 …

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 …

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 …

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

Take (n r) (n r). It denotes how in how many different ways you can choose r r elements from a set of k k elements. For case (43) (4 3) which evaluates to 4! 3!(4−3)! = 4 4! 3! (4 3)! = 4, it …

May 20, 2020 · Construct any subset S S of n n items as follows: We put n n items in a row and go through them one by one. For each item we either say yes or no to indicate whether it …