How many IP addresses can one find in the header of an IP packet?

There are two forms of IP addresses. the first IPv4, consists of numbers from 0 to 255 in each of four groupings separated by a decimal point. 192.168.1.1 for instance which is used for most routers. So the number of addresses will be 255 x 255 x 255 x 255. This is a 32 bit system and provides enough addresses for the population of Earth (plus or minus) as it was back then, over 4 billion. The second format is IPv6 which is a 128 bit system. It can support 3.4×1038 addresses. More than enough for the foreseeable future. So your answer depends on which IP packet standard you mean.