There's this exercise question that's completely stumping me.

Ok, so there's 3 types of cookies:

5 Chocolate Chip - (C)

7 Oatmeal - (O)

And 3 Peanut Butter - (P)

Two cookies are taken (without replacing them)

Now, I would say the set of possible solutions is

{CC, CO, CP, OC, OO, OP, PC, PO, PP}

So, 9 solutions

1) What's the chance both are chocolate chip?

Since this is only 1 of the 9 solutions, I would say 1/9

2) What's the chance one is oatmeal and the other is peanut butter?

There are 2 chances. OP and PO. So, I would say 2/9 .. except 2/9 isn't an answer! (It's multi choice)

3) Whats the chance the first is peanut butter and the second is chocolate chip?

Again, I'd say 1/9

4) What's the chance the first is oatmeal and the second is chocolate chip?

... Again, 1/9

But these have to be wrong. Firstly, #2 doesn't follow because 2/9 isn't an acceptable solution. And the rest just FEEL wrong.

So I started wondering if I had to look at the NUMBER of cookies.

If I do, there is about a 33% chance of getting chocolate chip, 46% chance of getting oatmeal, and a 20% chance of getting peanut butter.

But after you get 1 cookie, there's 3 different ways it could go! If it's a chocolate chip, suddenly you have less chance of getting a chocolate chip and more of the others! Should this even be considered? The way it's worded, it seems like both are taken at the same time.

Any help is appreciated

EDIT:

So, for the first question:

Cookie 1:

33% chance of chocolate chip

46% chance of oatmeal

20% chance of peanut butter

If a chocolate chip is taken, then

Cookie 2:

29% chance of chocolate chip

50% chance of oatmeal

21% chance of peanut butter

So what is the chance that you will get both chocolate chip?