Question

Discrete Math (MACM 101 Question)




I need to understand this notation:

permutation general formula : nPr = n! / (n - r)! n stands for the total number of things we have, but what about r ?

Answer 1

$r$ is the number of objects from the total $n$ objects that you want to permute.

For example, if I have the set of characters $\{a,b,c,d\}$, I can choose to permute any of up to 4 of the characters. Suppose I take just 2 of them. Then the formula predicts I should find ${}_4P_2=\dfrac{4!}{(4-2)!}=\dfrac{24}2=12$ possible permutations. Indeed, these are

$\begin{matrix}ab&ac&ad\\ba&bc&bd\\ca&cb&cd\\da&db&dc\end{matrix}$