Permutation

If the order of the results matter, then it is called a permutation.

Here you can still differentiate whether the number remains the same (with replacement) or always decreases by one (without replacement).

With replacement, order matters

From an urn with $n$ different balls, $k$ balls are drawn one after the other with replacement.
If the order matters, the number of possible combinations is $N$:

Example

A password consists of four letters. How many combinations are possible?

1. B: Letter (26 options each: A-Z)
   
   $n=\color{blue}{26}$ and $k=\color{red}{4}$


2. Structure: $\text{BBBB}$
   
   Combinations: $26\cdot26\cdot26\cdot26=\color{blue}{26}^\color{red}{4}$ $=456.976$

Without replacement, order matters

From an urn with $n$ different balls, $k$ balls are drawn in succession without replacement.
If the order matters, the number of possible combinations is $N$:

Example

In a horse race with 10 horses, the first 5 are bet. How many combinations are possible?

$10\cdot9\cdot8\cdot7\cdot6$ $=30.240$