A common definition of “utilitarianism” is “the greatest good for the greatest number of people”. It may be the case that Jeremy Bentham used this formulation, but it seems to make a distinction that may not — in some circumstances — result in doing an action that results in the greatest overall good.
Situation A: A public policy choice that would give a benefit to a group of people. Every person both needs the benefit AND would receive the same benefit no matter how many other people were in the program. At this point, it seems clear that including more people increases the good.
Situation B: A college professor has a choice, teach in a way that helps a few students or teach in a way that helps a much larger number of students. Clearly, teaching more students is the greatest overall good.
Situation C: A choice — give every student in my class $1 — OR give $500 to a worthy charity — whose purpose is to help individual families gain housing security. So a family would probably use my $500 as a deposit on an apartment whose rent they could afford. So — Assuming my class has 50 students in it and assuming that money can be equated to the good — in the first choice I distribute $50, in the second $500. More people get a small benefit from the $50, but one family unit gets a much larger benefit from the $500.
What all of these examples have in common is that the thing that ends up being the right thing to do is the net good done by the action, not helping the larger number of people.