My DD was 19 mths when I had DS and during my pregnancy and while DS was young we had a terrible problem with biting. She bit a friends little baby, random children, friends children, me and so on.
I googled it and it said between 1 in 5 and 1 in 10 children will bite at some point. So it is more common than you would think.
The reasons for biting could be attention seeking, teething, over excitement, frustration they learn it gets an explosive reaction, most likely a combination of the above.
I tried everything to stop her, the most successful was to pick her up, go and looking the crying child in the face and explain how sad and hurt the bitten child was, I would comfort the child, apologise to the mum etc, then get DD to find a toy to give the child to make them feel better. I did that every time and eventually it just stopped. At playgroups I shadowed her (DS in arms) to try and prevent incidents.
I think the less fuss you make the better, if they get a big reaction from you it encourages the behaviour, I am sure of it.
Good luck. One good thing is if any child has bitten one of mine subsequently (and they have) I brush it off easily. Often the hardest thing was dealing with the other mothers reaction, the bitten child was over it way before the mum had calmed down.