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=(4!)/((4-2)!)=\frac{24}2=12` possible permutations. Indeed, these are


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