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 …

May 20, 2020 · To reiterate... $2^n-1$ is a fine answer to its own question... the question of how many non-empty subsets a set has. $2^n$ is a fine answer to its own question... the question of how many …

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.

Explore related questions combinatorics binomial-coefficients See similar questions with these tags.

Jun 28, 2017 · This is the Binomial theorem: $$ (a+b)^n=\sum_ {k=0}^n {n\choose k}a^ {n-k}b^k.$$ I do not understand the symbol $ {n\choose k}.$ How do I actually compute this? What does this notation …

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 …

Jan 19, 2020 · Is there an explicit formula for the sum $$0\\binom{n}{0}+1\\binom{n}{1}+\\dots+n\\binom{n}{n} = \\sum_{k=0}^nk\\binom{n}{k}$$?

Jul 1, 2023 · This question is taken from A First Course in Probability (8e) by Ross. How many different arrangements can be formed from the letters PEPPER? I understand that there are $6!$ …

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 …