Naive Bayes Classification Example Given the following data:
$$\begin{array}{c|c|c|c|c|} 
\text{Instance} & \text{A} & \text{B} &\text{C} &\text{Class} \\ \hline
\text{1} & 1 & 2 & 1 & 1 \\ \hline
\text{2}& 0 & 0 & 1 & 1 \\ \hline
\text{3} & 2 & 1 & 2 & 2 \\ \hline
\text{4} & 1 & 2 & 1 & 2 \\ \hline
\text{5} & 0 & 1 & 2 & 1 \\ \hline
\text{6} & 2 & 2 & 2 & 2 \\ \hline
\text{7} & 1 & 0 & 1 & 1\\ \hline
\end{array}$$
Predit the class label for instance $(A=1, B=2, C=2)$ using naive Bayes classifcation. 
Let $C_{1}$ be class $1$ and $C_{2}$ be class $2$.
I have so far that the class prior probabilties are:
$$P(C_{1})=\dfrac{4}{7}$$ $$P(C_{2})=\dfrac{3}{7}$$
Using Bayes Theorem: $$P(C{i}|X)=\dfrac{P(X|C{i})P(C_{i})}{P(X)}$$
I know that $P(X|C_{i})=\prod^{n}_{k=1}P(X_{k}|C_{i})$ but not sure how to calculate this.
Where do I go from here to go about answering the question?

For $C_1$, by the assumption of Naive Bayesian Classifier, we have
$$
P(A = 1, B = 2, C=2 \mid C_1) = P(A = 1 \mid C_1) \cdot P(B = 2 \mid C_1) \cdot P(C = 2 \mid C_1)
$$
Take $P(A = 1 \mid C_1)$ as an example. There are $4$ training records of $C_1$, among which there are $2$ records with $A = 1$. Therefore, $P(A = 1 \mid C_1) = \frac{2}{4}$. Similarly, you can calculate $P(B = 2 \mid C_1)$ and $P(C = 2 \mid C_1)$.
It is similar to calculate $P(A = 1, B = 2, C = 2 \mid C_2)$.
