\(P[\text{3rd 6 on roll 10}]=P[\text{2 6's in 9 rolls and a 6 on the 10th roll}=\\ \dbinom{9}{2}\left(\dfrac 1 6\right)^2 \left(\dfrac 5 6\right)^7 \cdot \dfrac 1 6 = \dfrac{78125}{1679616}\)
\(P[\text{3rd 6 on roll 10}]=P[\text{2 6's in 9 rolls and a 6 on the 10th roll}=\\ \dbinom{9}{2}\left(\dfrac 1 6\right)^2 \left(\dfrac 5 6\right)^7 \cdot \dfrac 1 6 = \dfrac{78125}{1679616}\)
