We have n actors. Each actor chooses from n*2 actions. How can I calculate the probability that at least one actor will choose a unique outcome?

For example, say we have 5 pickup artists in a town with 10 bars. Each PUA chooses a bar at random. What are the odds that at least one PUA will have a bar to himself/herself? 

This is relevant to some work I'm doing on scheduling in a distributed system. I know that the relevant equation should probably start with $\binom{n + 2n -1}{n}$, but then what?

unique() indeed answers your question, but another related and interesting function to achieve the same end is duplicated().

It gives you the possibility to look up which rows are duplicated.

a <- c(rep("A", 3), rep("B", 3), rep("C",2))
b <- c(1,1,2,4,1,1,2,2)
df <-data.frame(a,b)

duplicated(df)
[1] FALSE  TRUE FALSE FALSE FALSE  TRUE FALSE  TRUE

> df[duplicated(df), ]
  a b
2 A 1
6 B 1
8 C 2

> df[!duplicated(df), ]
  a b
1 A 1
3 A 2
4 B 4
5 B 1
7 C 2

