Question : What is the probability of getting a $9$ exactly once in $3$ throws with a pair of dice?
My Try: There are five possibilities: $(4,5), (5,4), (3,3), (6,3), (3,6)$.
Therefore, Probability is $\frac{5}{36}$ in a single throw.
Using Binomial Distribution
$$\binom{3}1 \cdot \bigg(\frac{5}{36}\bigg)^1 \cdot \bigg(\frac{31}{36}\bigg)^2$$
Answer: $0.308$
The book's answer is $64/243 = 0.26$ which is slightly less so I wonder whether I have missed out on some detail. Any help would be appreciated.