Creating result groups in R, using each element once (combination without repetition) - r

Question

I have a dataset of 6 individuals: A,B,C,D,E,F
I want to group these into two groups of three individuals and have done so with the combn function in R:
m <- combn(n, 3)
This gives me all 20 possible groups where individuals occur in multiple groups. From this set of groups I then went to find all possible combinations of results, where each individual can only be used once.
I would like to do this using combinations without repetition:
C(n,r) = n! / r!(n-r)! and would therefore get 10 results that would look like this:
abc + def
abd + cef
abe + cdf
abf + cde
acd + bef
ace + bdf
acf + bde
ade + bcf
adf + bce
aef + bcd
I am not sure how to code this in R, from the list of groups that I have generated.
Edit: to generate the dataset I am using I have used the following code:
individuals <- c("a","b","c","d","e","f")
n <- length(individuals)
x <- 3
comb = function(n, x) {
factorial(n) / factorial(n-x) / factorial(x)
}
comb(n,x)
(m <- combn(n, 3))
numbers <- m
letters <- individuals
for (i in 1:length(numbers)) {
m[i] <- letters[numbers[i]]
}

Answer 1

In base R:
Create combnations of 3 letters and store it in a list (asplit)
Create new combnations of 2 groups (of 3 letters)
Filter the list to only keep combinations where the both parts have no element in common
individuals <- c("a","b","c","d","e","f")
combn(individuals, 3, simplify = FALSE) |>
combn(m = 2, simplify = FALSE) |>
Filter(f = \(x) !any(x[[1]] %in% x[[2]]))
output
[[1]]
[[1]][[1]]
[1] "a" "b" "c"
[[1]][[2]]
[1] "d" "e" "f"
[[2]]
[[2]][[1]]
[1] "a" "b" "d"
[[2]][[2]]
[1] "c" "e" "f"
[[3]]
[[3]][[1]]
[1] "a" "b" "e"
[[3]][[2]]
[1] "c" "d" "f"
[[4]]
[[4]][[1]]
[1] "a" "b" "f"
[[4]][[2]]
[1] "c" "d" "e"
[[5]]
[[5]][[1]]
[1] "a" "c" "d"
[[5]][[2]]
[1] "b" "e" "f"
[[6]]
[[6]][[1]]
[1] "a" "c" "e"
[[6]][[2]]
[1] "b" "d" "f"
[[7]]
[[7]][[1]]
[1] "a" "c" "f"
[[7]][[2]]
[1] "b" "d" "e"
[[8]]
[[8]][[1]]
[1] "a" "d" "e"
[[8]][[2]]
[1] "b" "c" "f"
[[9]]
[[9]][[1]]
[1] "a" "d" "f"
[[9]][[2]]
[1] "b" "c" "e"
[[10]]
[[10]][[1]]
[1] "a" "e" "f"
[[10]][[2]]
[1] "b" "c" "d"