For the record, the common definition of Utilitarianism as "the greatest good for the greatest number of people" is both popular and an incorrect synopsis of Mill's theory.
With this definition you can be forced to do that which benefits more individual people instead of doing what is the greatest good.
For example, if you can make 50 people slightly happy with action A, but move one person from extreme pain to extreme happiness with action B. The formulation that entails making the greatest NUMBER of people happy means you do action A (because 50 people is more than 1 person) -- when, in fact the greatest utility (change from pain to pleasure, i.e. increase in pleasure) comes from action B.
Careful reading of Mill -- hell, a cursory reading of Mill -- shows that Mill is concerned with the net increase in happiness. To calculate this increase, all impacted persons must have their pleasures and pains considered -- but, this does not entail his position was "the greatest good for the greatest number of people".
This is one of my biggest pet-peeves -- and the easiest way to know that my students are using the internet instead of class notes when writing a paper or exam. I thought I'd write this post in the hopes that the argument against this flawed definition will be out there... Along those lines, the argument that 'most people use this synopsis' is committing the basic ad populum fallacy... I suppose it is easier to say "everyone is doing it" than to actually read and think critically about Mill.