Q:

Calculate that at least n number of x values occur from multinomial distribution

Let's say X can take on 5 values
X<-1:5

each of the 5 values occur with some probability:
p<-c(0.2,0.3,0.1,0.3,0.1), where sum(p)=1
I would like to get the probability that number 5 occurs at least 2 times out of 3 trials.
For the binomial case I would use:
sum(dbinom(2:3,3,0.1))

What is the equivalent of this in the multinomial case?
I know that the equivalent command is dmultinom(), but I don't understand what the equivalent arguments are. 
dmultinom(x,size,prob)

I don't understand what would correspond to 'at least 2 out of 3'

A:

If $X_5$ is the number of times '5' occurs in 3 trials, you could do it with the multinomial probability function by computing $1-P(X_5=0)-P(X_5=1)$, but to get those probabiltiies you'd need to sum over all the arrangements of the other values. That's a minor nuisance (but it can be done for this small case easily enough).
You can do it as a binomial. Note that you either get a result of 5 or you don't, and it doesn't matter for this question which other categories occur. With the binomial, you can do the sum more directly, since cumulative probabilities are available.

So in R you could use dmultinom to do it the first way and you could use pbinomial to do it the second way.

