MathDB

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{}

Problem Statement