A calculus of the absurd

16.2 Finding the number of permutations

How many ways can we arrange distinct people in a straight line? For \(n\) people in a straight line, we can put \(n\) people in the first position, \(n-1\) people in the second position, \(n-2\) in the third, and so on. Overall, then the number of ways of arranging distinct people in a line is equal to

\begin{equation} (n)(n-1)(n-2)...1 = n! \end{equation}