Proposition 7.2.1
Let and be two finite and non empty sets; we denote and .The number of mappings from to is equal to .

Proof.
Denote the elements of by
and let
be a mapping. For any index such that
, we have possible choices for . As every choice is independent from the other ones, the total number of possibilities is
.

The following tree represents the choices for a mapping from to whenh ::

Figure 1:
Mappings from a finite set to a finite set

For example, at a tea-room, they offer 9 different kinds of tea. Five people
order a cup of tea; there are
different possibilities of service.
root
2002-06-10