A question about permutation?

Question

If Y is a non-empty set and a, b are permutation of Y, prove that
A o B is also a permutation of Y.

Answer 1

A permutation of a set Y is any function

f: Y --> Y

If a, b are such functions, then

a o b : Y --> Y --> Y

is a well defined composition (because co-domain of a is contained in domain of b), so it is also a permutation of Y.

Answer 2

A permutation is an arrangement of items (in all possible ways). For example, the permutations of the numbers 1, 2 and 3 are:
123, 132, 213, 231, 312 and 321

So there are six possible permutations of 1, 2 and 3.

The number of permutations of any group of items can be quickly found by using the following rule:
number of permutations of n different items = n ! (pronounced n factorial).

remember that a permutation of Y is what gives Y or creates it so if a, b are functions of Y, well therefor

A o B : Y --> Y --> Y