The distribution of roll of a dice $12$ times

Question

What's the distribution of a variable $X$ if $X$ represents the number of times you get outcome $k$ when you roll a dice $12$ times?

I thought that the distribution was a binomial distribution with $n=12$ and $p=\dfrac16$, but it seems to be wrong?

Answer 1

$$\forall{k\in[1\dots6],n\in[0\dots12]}:P_k(X=n)=\frac{\binom{12}{n}\cdot5^{12-n}}{6^{12}}=\binom{12}{n}\cdot\left(\frac16\right)^{n}\cdot\left(\frac56\right)^{12-n}$$