For starters, forgive my math terminology ignorance (I'll edit this question, once errors in my vocabulary are pointed out).
How can I print a complete set of 3 element permutation of a 10 element vector in R?
Let's assume a vector consists of 10 unique letters A to J
x<- LETTERS[seq( from = 1, to = 10 )]
This can be easily done using the gtools package.
prm <- gtools::permutations(n=10, r=3, v=LETTERS[1:10])
Then you can apply paste0 across the rows to get a vector.
apply(prm, 1, function(x)paste0(x, collapse=''))