2003
Problem - 2824
Pat is to select six cookies from a tray containing only chocolate chip, oatmeal, and peanut butter cookies. There are at least six of each of these three kinds of cookies on the tray. How many different assortments of six cookies can be selected?
Answer
$28$
This is equivalent to counting the number of non-negative integer solutions to the following equation $$x + y + z = 6$$
where $x$, $y$, and $z$ represent the number of the three types of cookies, respectively. The answer as $$\binom{6 + 3 - 1}{3-1}=\boxed{28}$$