Usually the complete set of primary (baby) teeth are erupted by 30 months of age.
If your 3 year old is have pain, he/she could be late with tooth eruption. However, we usually see 3 year olds with their full compliment of baby teeth, so the pain could be something else e.g. Decay, ulcerations etc. You should bring your child to a pediatric dentist to find out what is happeneing.