So the problem is the following:
Given a complete deck of 52 cards, 9 cards are drawn one by one with reposition.What is the probability that in a hand (of 9 cards) in which 3 aces come out, the 3rd will come out at the j'th draw?
My answer:
I was able to reach the correct answer (according to the solutions to the exercise) for the 9'th draw, which is
$$\binom{8}{2}\left(\frac{4}{52}\right)^3\left(\frac{48}{52}\right)^6$$
My thinking being: Probability of getting 2 aces in the first 8 cards times the probability of getting an ace in the 9'th (and last) card.
For the j'th draw I ended up with the following answer:
$$\binom{j-1}{2}\left(\frac{4}{52}\right)^3\left(\frac{48}{52}\right)^6$$
The thinking being very similar to the one I used before. According to the solution this is wrong. The correct answer should be:
$$\binom{j-1}{2}\left(\frac{4}{52}\right)^3\left(\frac{48}{52}\right)^{j-3}$$
Where did I go wrong? Did they actually mean "at least 3 aces"?
