# combinatorics's questions - Chinese 1answer

33.156 combinatorics questions.

### How many 3 letter words possible with the word Abacus?

I am having difficulty solving this. I know that 6 letter words possible with abacus is (6! / 2! ). But my doubt is what happens when we have to choose 3 letters from abacus and how will we handle the ...

### 5 Why does the Fibonacci sequence seem to have such a rich theory?

Pick four integers $a,b,c$ and $d$. Then we get a corresponding sequence given by $$t_{n+2} = at_{n+1} +bt_n, \; t_1 = c, \;t_2 = d.$$ From what I can tell, we seem to get an especially rich theory ...

### 1 Probability of a structure of consecutive head tosses

The exercise: A group of N friends sits around a table shaped as a regular polygon with N sides, one person on each side. Everyone tosses a fair coin once and a person is called positive if she and ...

### 2 Prove: the number of simple undirected graphs with n different nodes, s.t every node has even degree is $2^\binom{n-1}{2}$

1 answers, 39 views combinatorics graph-theory

### 14 How many triangles can be formed by the vertices of a regular polygon of n sides?

How many triangles can be formed by the vertices of a regular polygon of $n$ sides? And how many if no side of the polygon is to be a side of any triangle ? I have no idea where I should start to ...

### 2 Counting non-nesting multi-permutations

Given a sequence $1,1,2,2,3,3, …,k,k$, I am interested in counting the number of non-nesting permutations of the above sequence. Two intervals (determined by symbols $K$ and $L$) are nesting if one is ...

### 1 Non-uniform distribution with uniform subsets

Let $X=[X_1, \dots, X_n]$ be a random vector of binary-valued random variables, taking values in $\{0,1\}^n$. Let $S(n,k)$ denote the set of all size $k$ subsets of $\{1,\dots,n\}$. Can anyone ...

### 4 What is the expected number of suits in a hand of 4 cards?

3 answers, 1.148 views probability combinatorics poker