After asking I remembered seeing it somewhere...
Powerpoint
LINK Page 9
(hopefully this is accurate data)
Branch/#Allocations/#1st Choice/Odds for 1st choice
Aviation Officer AV 133/239/0.56
Medical Service MS 190/308/0.62
Military Police MP 94/149/0.63
Infantry Officer IN 275/426/0.65
Finance Officer FI 35/50/0.70
Armor Officer AR 124/175/0.71
Military Intelligence MI 346/457/0.76
Signal Officer SC 235/171/1.37
Field Artillery Officer FA 178/110/1.62
Adjutant General AG 139/64/2.17
Air Defense Artillery AD 68/30/2.27
Quartermaster Officer QM 152/62/2.45
Engineer Officer EN 166/214/4.42
Chemical Officer CM 53/12/4.42
Ordnance Officer OD 165/34/4.85
Transportation Officer TC 183/35/5.22