Table of Contents

Number Of Permutations

Problem

Given finite set $X$ with $n$ elements, how many permutations are there of $X$?

  1. Show that if $X=\{1\}$, then there is only one permutation of $X$.
  2. Show that if $X=\{1,2\}$, then there are two permutations of $X$. List them.
  3. Make a list of all permutations of $X=\{1,2,3\}$, and then of $X=\{1,2,3,4\}$. What pattern do you see?
  4. Make a conjecture about the number of permutation of $X$ if $|X|=n$. Then prove your conjecture.

Remarks

$\LaTeX$ version

problem.number_of_permutations.tex
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% RequiredPackages: \usepackage{tikz}
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\begin{problem}
Given finite set $X$ with $n$ elements, how many permutations are there of $X$?
\begin{enumerate}
Show that if $X=\{1\}$, then there is only one permutation of $X$.
\item Show that if $X=\{1,2\}$, then there are two permutations of $X$. List them.
\item Make a list of all permutations of $X=\{1,2,3\}$, and then of $X=\{1,2,3,4\}$. What pattern do you see?
\item Make a conjecture about the number of permutation of $X$ if $|X|=n$. Then prove your conjecture.
\end{problem}

problem ben