Next: Arrangements Up: Elementary combinatorics Previous: Elementary combinatorics   Contents

## Mappings from a finite set to a finite set

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 ::

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