Some stats on the massive "coalition of the willing" list.
Armenia has 46 soldiers, medical and logistical support. Albania has 125 non-combat troops. Australia has 450 troops - 120 are assigned to protecting their embassy. Apart from the US and UK, the highest numbers of troops supplied by other countries is from Korea - with a total of 3300 - who are engaged on repairing infrastructure, but currently being withdrawn.
The moment any country offers to send a military vet to Iraq to take care of zoo animals, you are assured that country will end up on the "coalition of the willing" list
