The natural numbers $k \geqslant n$ are given. Peter has $n{}$ objects and $N{}$ special ways in which he likes to lay them out in a row from left to right. He noticed that for any non-empty subset $A{}$ of these objects containing $|A| \leqslant k$ objects, and any element $a\in A$, there are exactly $N/|A|$ special ways for which element $a{}$ is the leftmost in the set $A{}$. Prove that, under the same conditions on $A{}$ and $a{}$, for any integer $m =1,2,\ldots,|A|$ there are exactly $N/|A|$ special ways for which the element $a{}$ is the $m^{\text{th}}$ from the left in the set $A{}$.