**Proposition 7.2.3**
Let

and

be two finite sets such that

and

,
where

and

are two integers verifiying the inequalities:

. The set of all the injections

is
finite and its cardinality is equal to

.

*Proof*.
Denote the elements of

by

and let

be an injection from

to

. For

we have

possible choices; for

, we have

choices, and so on. As the choices alreday made have no other influence on the further ones than the impossibility of chosing once again the same element in

as an image, the total number of choices is the product

.