Number of permutations of n distinct objects when a particular object is always included in any arranegement

Question

In this theorem I understand that if there are n objects and r number of objects are taken at a time and if any one object is always included in any arrangement then what we do is ($n-1!/r-1!$)-(i) but why in the formula are we multiplying (i) by r?

Answer 1

Because the order matters.

After we choose $r-1$ of them out of the remaining $n-1$ iterms. We first sort the order.

After which, we still need to decide a position for the special object, there are $r$ options for the position of the object, hence by multiplication principle, we multiply by $r$.