The problem is as follows:
Draw cards at random with replacement from a standard deck of cards. Given that face cards are Jack, Queen and King, what is the probability that the 3rd face card is drawn on the 8th draw?
The correct answer given is ${7 \choose 2}(\frac{3}{13} )^3(\frac{10}{13})^5 $ But I don't understand why taking the probability of getting 3 successes out of 8 which is ${8 \choose 3}(\frac{3}{13} )^3(\frac{10}{13})^5$ And subtracting the probability of having 3 successes in seven ${7 \choose 3}(\frac{3}{13} )^3(\frac{10}{13})^4$ Yielding ${8 \choose 3}(\frac{3}{13} )^3(\frac{10}{13})^5-{7 \choose 3}(\frac{3}{13} )^3(\frac{10}{13})^4$ is incorrect. It makes sense to me intuitively. Can someone help me understand this please?