To generate all combinations of elements from a pair or multiples of vectors, use expand.grid().
expand.grid(c(1:3), LETTERS[1:3])
Var1 Var2
1 1 A
2 2 A
3 3 A
4 1 B
5 2 B
6 3 B
7 1 C
8 2 C
9 3 C
expand.grid(c(1:3),LETTERS[1:3],letters[1:2])
Var1 Var2 Var3
1 1 A a
2 2 A a
3 3 A a
4 1 B a
5 2 B a
6 3 B a
7 1 C a
8 2 C a
9 3 C a
10 1 A b
11 2 A b
12 3 A b
13 1 B b
14 2 B b
15 3 B b
16 1 C b
17 2 C b
18 3 C b