x <- matrix(c(letters[1:10], LETTERS[1:10]), 2, byrow = T)
print(x)
#      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
# [1,] "a"  "b"  "c"  "d"  "e"  "f"  "g"  "h"  "i"  "j"  
# [2,] "A"  "B"  "C"  "D"  "E"  "F"  "G"  "H"  "I"  "J"  
ind <- as.matrix(expand.grid(replicate(10, 1:2, simplify = F)))
res <- t(apply(ind, 1, function(k) {
  diag(x[k,])
}))
head(res)
#      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
# [1,] "a"  "c"  "e"  "g"  "i"  "k"  "m"  "o"  "q"  "s"  
# [2,] "b"  "c"  "e"  "g"  "i"  "k"  "m"  "o"  "q"  "s"  
# [3,] "a"  "d"  "e"  "g"  "i"  "k"  "m"  "o"  "q"  "s"  
# [4,] "b"  "d"  "e"  "g"  "i"  "k"  "m"  "o"  "q"  "s"  
# [5,] "a"  "c"  "f"  "g"  "i"  "k"  "m"  "o"  "q"  "s"  
# [6,] "b"  "c"  "f"  "g"  "i"  "k"  "m"  "o"  "q"  "s"  
tail(res)
#         [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
# [1019,] "a"  "B"  "c"  "D"  "E"  "F"  "G"  "H"  "I"  "J"  
# [1020,] "A"  "B"  "c"  "D"  "E"  "F"  "G"  "H"  "I"  "J"  
# [1021,] "a"  "b"  "C"  "D"  "E"  "F"  "G"  "H"  "I"  "J"  
# [1022,] "A"  "b"  "C"  "D"  "E"  "F"  "G"  "H"  "I"  "J"  
# [1023,] "a"  "B"  "C"  "D"  "E"  "F"  "G"  "H"  "I"  "J"  
# [1024,] "A"  "B"  "C"  "D"  "E"  "F"  "G"  "H"  "I"  "J"  

dim(res)   # totally 1024 combinations


res[1, ]
res[2, ]
#...
res[1024, ]