**Explanation:**

Of the 6 cookies Pat chooses, there are three types: chocolate chip, oatmeal, and peanut butter cookies. We also note that there can be 0 of a type. We can use the stars and bars formula to divide 6 objects into three categories (n is the number of objects, which is cookies in this case, and k is the number of categories):

n+k-1 choose k-1

= 6+3-1 choose 3-1

= 8 choose 2

= 28

That is why the answer is 28.

**Please find below the proof for the stars and bars formula.**

Let's use the cookies problem from above to help us with the proof. Right now, n=6 (6 cookies) and k=3 (3 types of cookies).

Putting 6 cookies into 3 categories looks like this:

costume1.png

There are 8 objects total in that picture (6 cookies + 2 bars).

Let's say we remove all objects and hold them. There are 8 spots to put our 8 objects. We can choose 2 spots of these 8 spots to put our bars, and the cookies go into the remaining 6 spots. Therefore, there are 8 choose 2 = 28 different combinations of 6 cookies.

So, in the formula n+k-1 choose k-1, n+k-1 represents the total number of spots to put the objects and the bars, and k-1 represents the number of bars needed to split the objects into k categories (for example, in our problem, 2 bars were needed to split the 6 cookies into 3 categories).