Question

In how many ways can$r$objects be selected from a set of $n$objects if the order of selection is considered relevant?

Short answer

Choose the first, then the second, and so on...

$\frac{n!}{(n-r)!}$

Step-by-step solution

Given Information.

$r$objects are selected from a set of $n$objects if the order of selection is considered relevant.

Explanation.

Choosing$r$from$n$, ordered

The first element can be selected in $n$ways

The second can be any of the remaining $n-1$

The $r$element can be any of the$n-r+1$elements.

By the generalized principle of the product, there are$n·(n-1)·\dots (n-r+1)=\frac{n!}{(n-r)!}$possible choices.