Two arguments to calloc

I heard two [mutually exclusive] explanations for why it has two arguments:

1. calloc takes the responsibility for checking for overflow on multiplication. If the total size of the requested block is too large (like overflows size_t), calloc returns null pointer to indicate failure. With malloc you have to watch for overflow yourself, which many people simply forget to do. (Although the history of standard library knows examples of calloc implementations that ignored overflow, and thus worked incorrectly).

2. calloc actually allows one to allocate bigger blocks of memory than the range of type size_t, i.e. calloc might be capable of performing the proper non-overflowing large multiplication of its arguments and allocate the block of the resultant size. For this reason, since calloc uses two arguments of type size_t, it can allocate bigger blocks than malloc will ever be able to (since malloc takes only one argument of type size_t).

I always believed that the first explanation is the right one. However, after reading some posts here on SO I have my doubts.