Create Combinations in R by Groups

Question

I want to create a list for my classroom of every possible group of 4 students. If I have 20 students, how I can I create this, by group, in R where my rows are each combination

Answer 1

Here's an example for smaller numbers. I don't think this will scale well for 20 students

total_students = 4
each_group = 2
total_groups = total_students/each_group

if (total_students %% each_group == 0) {
    library(arrangements)

    group_id = rep(1:total_groups, each = each_group)

    #There is room to increase efficiency here by generating only relevant permutations
    temp = permutations(1:total_students, total_students)
    temp = unique(t(apply(temp, 1, function(i) {
        x = group_id[i]
        match(x, unique(x))
    })))

    dimnames(temp) = list(COMBO = paste0("C", 1:NROW(temp)),
                          Student = paste0("S", 1:NCOL(temp)))
} else {
    cat("Total students not multiple of each_group")
    temp = NA
}
#> Warning: package 'arrangements' was built under R version 3.5.3
temp
#>      Student
#> COMBO S1 S2 S3 S4
#>    C1  1  1  2  2
#>    C2  1  2  1  2
#>    C3  1  2  2  1

^{Created on 2019-09-02 by the reprex package (v0.3.0)}

The total number of possible ways is given by following function (from here)

foo = function(N, k) {
    #N is total number or people, k is number of people in each group
    if (N %% k == 0) {
        m = N/k
        factorial(N)/(factorial(k)^m * factorial(m))
    } else {
        stop("N is not a multiple of n")
    }
}

foo(4, 2)
#[1] 3

foo(20, 4)
#[1] 2546168625

For groups of 4 people from a total of 20 people, the number of possible arrangements is massive.