This is a combination of 27 elements taken 2 at a time, which produces 351 unique results. This is distinct from a permutation of 27 elements, which take into account order. That's equal here to 27^2 = 729.
combn(27,2)
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,] 1 1 1 1 1 1 1 1 1 1 1 1 1 1
#> [2,] 2 3 4 5 6 7 8 9 10 11 12 13 14 15
#> [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
#> [1,] 1 1 1 1 1 1 1 1 1 1 1 1
#> [2,] 16 17 18 19 20 21 22 23 24 25 26 27
#> [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]
#> [1,] 2 2 2 2 2 2 2 2 2 2 2 2
#> [2,] 3 4 5 6 7 8 9 10 11 12 13 14
#> [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50]
#> [1,] 2 2 2 2 2 2 2 2 2 2 2 2
#> [2,] 15 16 17 18 19 20 21 22 23 24 25 26
#> [,51] [,52] [,53] [,54] [,55] [,56] [,57] [,58] [,59] [,60] [,61] [,62]
#> [1,] 2 3 3 3 3 3 3 3 3 3 3 3
#> [2,] 27 4 5 6 7 8 9 10 11 12 13 14
#> [,63] [,64] [,65] [,66] [,67] [,68] [,69] [,70] [,71] [,72] [,73] [,74]
#> [1,] 3 3 3 3 3 3 3 3 3 3 3 3
#> [2,] 15 16 17 18 19 20 21 22 23 24 25 26
#> [,75] [,76] [,77] [,78] [,79] [,80] [,81] [,82] [,83] [,84] [,85] [,86]
#> [1,] 3 4 4 4 4 4 4 4 4 4 4 4
#> [2,] 27 5 6 7 8 9 10 11 12 13 14 15
#> [,87] [,88] [,89] [,90] [,91] [,92] [,93] [,94] [,95] [,96] [,97] [,98]
#> [1,] 4 4 4 4 4 4 4 4 4 4 4 4
#> [2,] 16 17 18 19 20 21 22 23 24 25 26 27
#> [,99] [,100] [,101] [,102] [,103] [,104] [,105] [,106] [,107] [,108]
#> [1,] 5 5 5 5 5 5 5 5 5 5
#> [2,] 6 7 8 9 10 11 12 13 14 15
#> [,109] [,110] [,111] [,112] [,113] [,114] [,115] [,116] [,117] [,118]
#> [1,] 5 5 5 5 5 5 5 5 5 5
#> [2,] 16 17 18 19 20 21 22 23 24 25
#> [,119] [,120] [,121] [,122] [,123] [,124] [,125] [,126] [,127] [,128]
#> [1,] 5 5 6 6 6 6 6 6 6 6
#> [2,] 26 27 7 8 9 10 11 12 13 14
#> [,129] [,130] [,131] [,132] [,133] [,134] [,135] [,136] [,137] [,138]
#> [1,] 6 6 6 6 6 6 6 6 6 6
#> [2,] 15 16 17 18 19 20 21 22 23 24
#> [,139] [,140] [,141] [,142] [,143] [,144] [,145] [,146] [,147] [,148]
#> [1,] 6 6 6 7 7 7 7 7 7 7
#> [2,] 25 26 27 8 9 10 11 12 13 14
#> [,149] [,150] [,151] [,152] [,153] [,154] [,155] [,156] [,157] [,158]
#> [1,] 7 7 7 7 7 7 7 7 7 7
#> [2,] 15 16 17 18 19 20 21 22 23 24
#> [,159] [,160] [,161] [,162] [,163] [,164] [,165] [,166] [,167] [,168]
#> [1,] 7 7 7 8 8 8 8 8 8 8
#> [2,] 25 26 27 9 10 11 12 13 14 15
#> [,169] [,170] [,171] [,172] [,173] [,174] [,175] [,176] [,177] [,178]
#> [1,] 8 8 8 8 8 8 8 8 8 8
#> [2,] 16 17 18 19 20 21 22 23 24 25
#> [,179] [,180] [,181] [,182] [,183] [,184] [,185] [,186] [,187] [,188]
#> [1,] 8 8 9 9 9 9 9 9 9 9
#> [2,] 26 27 10 11 12 13 14 15 16 17
#> [,189] [,190] [,191] [,192] [,193] [,194] [,195] [,196] [,197] [,198]
#> [1,] 9 9 9 9 9 9 9 9 9 9
#> [2,] 18 19 20 21 22 23 24 25 26 27
#> [,199] [,200] [,201] [,202] [,203] [,204] [,205] [,206] [,207] [,208]
#> [1,] 10 10 10 10 10 10 10 10 10 10
#> [2,] 11 12 13 14 15 16 17 18 19 20
#> [,209] [,210] [,211] [,212] [,213] [,214] [,215] [,216] [,217] [,218]
#> [1,] 10 10 10 10 10 10 10 11 11 11
#> [2,] 21 22 23 24 25 26 27 12 13 14
#> [,219] [,220] [,221] [,222] [,223] [,224] [,225] [,226] [,227] [,228]
#> [1,] 11 11 11 11 11 11 11 11 11 11
#> [2,] 15 16 17 18 19 20 21 22 23 24
#> [,229] [,230] [,231] [,232] [,233] [,234] [,235] [,236] [,237] [,238]
#> [1,] 11 11 11 12 12 12 12 12 12 12
#> [2,] 25 26 27 13 14 15 16 17 18 19
#> [,239] [,240] [,241] [,242] [,243] [,244] [,245] [,246] [,247] [,248]
#> [1,] 12 12 12 12 12 12 12 12 13 13
#> [2,] 20 21 22 23 24 25 26 27 14 15
#> [,249] [,250] [,251] [,252] [,253] [,254] [,255] [,256] [,257] [,258]
#> [1,] 13 13 13 13 13 13 13 13 13 13
#> [2,] 16 17 18 19 20 21 22 23 24 25
#> [,259] [,260] [,261] [,262] [,263] [,264] [,265] [,266] [,267] [,268]
#> [1,] 13 13 14 14 14 14 14 14 14 14
#> [2,] 26 27 15 16 17 18 19 20 21 22
#> [,269] [,270] [,271] [,272] [,273] [,274] [,275] [,276] [,277] [,278]
#> [1,] 14 14 14 14 14 15 15 15 15 15
#> [2,] 23 24 25 26 27 16 17 18 19 20
#> [,279] [,280] [,281] [,282] [,283] [,284] [,285] [,286] [,287] [,288]
#> [1,] 15 15 15 15 15 15 15 16 16 16
#> [2,] 21 22 23 24 25 26 27 17 18 19
#> [,289] [,290] [,291] [,292] [,293] [,294] [,295] [,296] [,297] [,298]
#> [1,] 16 16 16 16 16 16 16 16 17 17
#> [2,] 20 21 22 23 24 25 26 27 18 19
#> [,299] [,300] [,301] [,302] [,303] [,304] [,305] [,306] [,307] [,308]
#> [1,] 17 17 17 17 17 17 17 17 18 18
#> [2,] 20 21 22 23 24 25 26 27 19 20
#> [,309] [,310] [,311] [,312] [,313] [,314] [,315] [,316] [,317] [,318]
#> [1,] 18 18 18 18 18 18 18 19 19 19
#> [2,] 21 22 23 24 25 26 27 20 21 22
#> [,319] [,320] [,321] [,322] [,323] [,324] [,325] [,326] [,327] [,328]
#> [1,] 19 19 19 19 19 20 20 20 20 20
#> [2,] 23 24 25 26 27 21 22 23 24 25
#> [,329] [,330] [,331] [,332] [,333] [,334] [,335] [,336] [,337] [,338]
#> [1,] 20 20 21 21 21 21 21 21 22 22
#> [2,] 26 27 22 23 24 25 26 27 23 24
#> [,339] [,340] [,341] [,342] [,343] [,344] [,345] [,346] [,347] [,348]
#> [1,] 22 22 22 23 23 23 23 24 24 24
#> [2,] 25 26 27 24 25 26 27 25 26 27
#> [,349] [,350] [,351]
#> [1,] 25 25 26
#> [2,] 26 27 27
Every R problem can be thought of with advantage as the interaction of three objects— an existing object, x , a desired object,y , and a function, f, that will return a value of y given x as an argument. In other words, school algebra— f(x) = y. Any of the objects can be composites.
Here x consists of 27 tests each with 2 possible outcomes. In practice, this would be represented by a data frame in which test subjects were rows, the 27 tests columns, and the entries either A or B. And y to be determined is the maximum number of different outcomes for the data frame results, which will be no greater than the number of test subjects—nrow(the_data_frame) or the return value of a function f that returns an object with all the possible outcomes, whichever is smaller.
In other words, if there are only 30 different subjects, there can be, at most, 30 different outcomes, but if there are 1,000, there can be as many as 351.
If you had to write f yourself, it might look like the available-for-free combn
function (x, m, FUN = NULL, simplify = TRUE, ...)
{
stopifnot(length(m) == 1L, is.numeric(m))
if (m < 0)
stop("m < 0", domain = NA)
if (is.numeric(x) && length(x) == 1L && x > 0 && trunc(x) ==
x)
x <- seq_len(x)
n <- length(x)
if (n < m)
stop("n < m", domain = NA)
x0 <- x
if (simplify) {
if (is.factor(x))
x <- as.integer(x)
}
m <- as.integer(m)
e <- 0
h <- m
a <- seq_len(m)
nofun <- is.null(FUN)
if (!nofun && !is.function(FUN))
stop("'FUN' must be a function or NULL")
len.r <- length(r <- if (nofun) x[a] else FUN(x[a], ...))
count <- as.integer(round(choose(n, m)))
if (simplify) {
dim.use <- if (nofun)
c(m, count)
else {
d <- dim(r)
if (length(d) > 1L)
c(d, count)
else if (len.r != 1L)
c(len.r, count)
else c(d, count)
}
}
if (simplify)
out <- matrix(r, nrow = len.r, ncol = count)
else {
out <- vector("list", count)
out[[1L]] <- r
}
if (m > 0) {
i <- 2L
nmmp1 <- n - m + 1L
while (a[1L] != nmmp1) {
if (e < n - h) {
h <- 1L
e <- a[m]
j <- 1L
}
else {
e <- a[m - h]
h <- h + 1L
j <- 1L:h
}
a[m - h + j] <- e + j
r <- if (nofun)
x[a]
else FUN(x[a], ...)
if (simplify)
out[, i] <- r
else out[[i]] <- r
i <- i + 1L
}
}
if (simplify) {
if (is.factor(x0)) {
levels(out) <- levels(x0)
class(out) <- class(x0)
}
dim(out) <- dim.use
}
out
}
But the whole point of working in R is that the user doesn't have to re-invent this wheel, just find it. A good place to start is rseek.org, a R-tuned front end to Google. Try searching for "combinations" there, for example.