Probability from rolling 4 sided die?

Question

I am unsure how to go about doing this question. Could a binomial probability distribution be applied to this?

Full question: Assuming I have a $4$ sided die (labeled $1,2,3,$ and $4$), with equal probability of landing on each side, and I roll the die $9$ times. What is the probability that I'll roll $1$ and $2$ $2-$times each, a $3$ $4-$times, and a $4$ $1-$time?

Answer 1

The number to distribute two ones, two twos, four threes and one four is multinomial coefficient $\binom{9}{2,2,4,1}$. There are $4^9$ possible sequences.