I want to buy few games here in Australia for my friend living in Serbia. He has an Xbox 360 bought over there. Will he be able to play them?
Yes. Both Australia and Serbia use PAL.
Related: this question regarding using a UK Xbox in Australia.
Note, I am assuming the Xbox picked up in Serbia is a standard PAL version and that the games you are sending are also PAL (i.e. work fine on an Australian Xbox). If the Xbox is an American import, for example, then it will depend on the game. Some games are region-locked (i.e. buying a game with NTSC on the box may only work in an American Xbox).