A jar contains n red and n green marbles

Question

I'm so confused with the question below and I do appreciate your help:)

A jar contains n red and n green marbles where n>=2. You pick two marbles from the jar.

Q: Number of ways to pick one of each color ( ) n^2

A.>

B.<

C.=

D.cannot be determined

I think the answer should be C, but it turns out to be A at least in my exercise book:(

Answer 1

They are counting red-green as different from green-red, so there are $2n^2$ ways to get one of each. I don't think the question is clear.

Answer 2

So, how many ways are there to pick marbles in general? First, (assuming without replacement), you choose the first marble from $2n$ marbles. Then, you choose the second marble. There are $2n-1$ marbles left. Thus, you hace $2n(2n-1)$ ways of choosing the marbles.

Next, consider choosing your first marble. It can be any color, so you have $2n$ choices - it doesn't matter which marble you choose. For the second marble, you MUST choose a different color. There are $2n-1$ marbles left, but $n$ of the color you didn't already choose. So you have $2n^2$ ways of choosing.

$2n^2>n^2$, so $A$ is, indeed, the answer.