Newbetuts

How many sequence of integers ($j_1 , j_2 , . . . , j_k$) are there such that $0 ≤ j_1 ≤ j_2 ≤ . . . ≤ j_k ≤ n$?

Poker and Combinatorics (Don't Mix): How to solve this problem?

An upper bound for $\sum_{i = 1}^m \binom{i}{k}\frac{1}{2^i}$?

Prove that $\sum\limits_{k=0}^{m}\binom{m}{k}\binom{n+k}{m}=\sum\limits_{k=0}^{m}\binom{n}{k}\binom{m}{k}2^k$ [duplicate]

The probability of rolling 5 dice ordered or unordered

Musical and combinatorial proof

10-digit numbers with constraints

How to find the sum $\sum_{k=1}^{\lfloor n/2\rfloor}\frac{2^{n-2k}\binom{n-2}{2k-2}\binom{2k-2}{k-1}}{k}$

$20$ people are sitting around a (circular) table. How many ways can we choose $3$ people, no two of whom are neighbors?

Expected value for advent of code (average case complexity)

A Curious Binomial Sum Identity without Calculus of Finite Differences

Any partition of $\{1,2,\ldots,100\}$ into seven subsets yields a subset with numbers $a,b,c,d$ such that $a+b=c+d$. [closed]

What are generating functions?

Given an array, how to generate all combinations of subset size k?

If $n\ge m$, then the number of $m$-cycles in $S_n$ is given by $\frac{n(n-1)(n-2)\cdots(n-m+1)}{m}$.

Number or regions formed when $n$ points on a circle are joined

New posts in combinatorics

Connections between topology and combinatorics

Combinations and Permutations of dice [closed]

Number of distinct nets of dual polyhedra

Confusion over probability problems

How many sequence of integers ($j_1 , j_2 , . . . , j_k$) are there such that $0 ≤ j_1 ≤ j_2 ≤ . . . ≤ j_k ≤ n$?

Poker and Combinatorics (Don't Mix): How to solve this problem?

An upper bound for $\sum_{i = 1}^m \binom{i}{k}\frac{1}{2^i}$?

Prove that $\sum\limits_{k=0}^{m}\binom{m}{k}\binom{n+k}{m}=\sum\limits_{k=0}^{m}\binom{n}{k}\binom{m}{k}2^k$ [duplicate]

The probability of rolling 5 dice ordered or unordered

Musical and combinatorial proof

10-digit numbers with constraints

How to find the sum $\sum_{k=1}^{\lfloor n/2\rfloor}\frac{2^{n-2k}\binom{n-2}{2k-2}\binom{2k-2}{k-1}}{k}$

$20$ people are sitting around a (circular) table. How many ways can we choose $3$ people, no two of whom are neighbors?

Expected value for advent of code (average case complexity)

A Curious Binomial Sum Identity without Calculus of Finite Differences

Any partition of $\{1,2,\ldots,100\}$ into seven subsets yields a subset with numbers $a,b,c,d$ such that $a+b=c+d$. [closed]

What are generating functions?

Given an array, how to generate all combinations of subset size k?

If $n\ge m$, then the number of $m$-cycles in $S_n$ is given by $\frac{n(n-1)(n-2)\cdots(n-m+1)}{m}$.

Number or regions formed when $n$ points on a circle are joined