# Recent questions tagged combinatory

5 votes
5 answers
1
Let $S$ be a set of consisting of $10$ elements. The number of tuples of the form $(A,B)$ such that $A$ and $B$ are subsets of $S$, and $A \subseteq B$ is ___________
5 votes
2 answers
2
There are $6$ jobs with distinct difficulty levels, and $3$ computers with distinct processing speeds. Each job is assigned to a computer such that: The fastest computer gets the toughest job and the slowest computer gets the easiest job. Every computer gets at least one job. The number of ways in which this can be done is ___________.
0 votes
1 answer
3
A permutation $\sigma$ is a bijection from the set $[n]=\{1,2,\dots ,n\}$ to itself. We denote it using the notation $\begin{pmatrix}1 & 2 & & n \\ {\sigma(1)} & {\sigma(2)} &\dots & {\sigma(n)} \end{pmatrix},$ e.g. if $n=3$ ... $\sigma =\begin{pmatrix} 1 & 2 & 3&4&5&6 \\ 2& 3&4&5&1&6 \end{pmatrix}, \; \tau=\begin{pmatrix} 1 & 2 & 3&4&5&6 \\ 4& 1&3&2&6&5 \end{pmatrix}$
0 votes
1 answer
4
A permutation $\sigma$ is a bijection from the set $[n]=\{1,2, ,n\}$ to itself. We denote it using the notation $\begin{pmatrix}1 & 2 & & n \\ {\sigma(1)} & {\sigma(2)} & & {\sigma(n)} \end{pmatrix},$ ... $|A_{\sigma} |$ and $|A_\tau|?$ Can you relate these with the signs of permutations $\sigma$ and $\tau ?$
1 vote
2 answers
5
What is the total number of ways to reach from $A$ to $B$ in the network given? $12$ $16$ $20$ $22$
2 votes
2 answers
6
How many ways are there to pack six copies of the same book into four identical boxes, where a box can contain as many as six books? $4$ $6$ $7$ $9$