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- STA256 Lecture 03

Permutations

Definition

$P_{r}^{n} = n (n - 1) (n - 2) \dots (n - r + 1) = \frac{n!}{(n - r)!}$

Example:
- Calculate the number of ways to select a president, vice president and treasurer from a group of $5$ people.
- Distinct titles
- $\begin{matrix} p e r s o n & 1 & 2 & 3 & 4 & 5 \\ p & v p & t \\ v p & p & t \\ \dots \end{matrix}$
- Because of the number of permutations, we can use the rules
- $P_{3}^{5} = \frac{5!}{(5 - 3)!} = \frac{120}{2} = 60$