Retreat question

[JJ_Colorado]

Hi,

I did a search but couldn't see a thread that addresses this although I'm sure it's been discussed before.

Scenario:
Provinces line up as follows with no other provinces (theoretically) on the map:
-A borders only B
-B borders A and C
-C borders only B
----so they are lined up A-B-C

-B and C are controlled by Enemy
-A is controlled by me
-A contains 2 of my armies, one flying, one walking

-Flying army flies from A to attack C
-Walking army walks from A to attack B

-Walking army wins battle
-Flying army loses battle and retreats

Are the battles executed in any particular (or random) order?
If battle in B is resolved before battle in C, will losers of battle in C be able to retreat to newly won province B?

Thanks,
John