Stars and bars allows us to count the number of ways to distribute 10 cookies to 3 kids and natural number solutions to \(x+y+z = 11\text{,}\) for example. A relatively easy modification allows us to put a lower bound restriction on these problems: perhaps each kid must get at least two cookies or \(x,y,z \ge 2\text{.}\) This was done by first assigning each kid (or variable) 2 cookies (or units) and then distributing the rest using stars and bars.
in-context