How many different ways can a person pick 6 cookies from a tray of 4 chocolate chip, 4 oatmeal, and 2 peanut butter cookies?
*assume that cookies of the same type are identical.
There are a total of 4+4+2=10 cookies. We want to pick 6 of them, so the total number of ways to do this is (610)=10!/6!4!=210.
However, we need to divide this number by 3! because the order in which we pick the cookies does not matter. (For example, picking a chocolate chip cookie, then an oatmeal cookie, and then a peanut butter cookie is the same as picking a peanut butter cookie, then an oatmeal cookie, and then a chocolate chip cookie.) So the final answer is 210/3!=35.