# Can three regular languages be concatenated?

If you have three languages $L_1=\{a,b\}, L_2=\{c,d\}, L_3 =\{e,f\}$, can they be concatenated?
If yes, would you concatenate the first two and concatenate the result to the third one or would you concatenate it as $\{ace, ade, acf, adf, bce, \ldots\}$? And what if one of the languages only contained the empty word $ε$?
Concatenation is associative: $$(L_1L_2)L_3 = L_1(L_2L_3) = \{w_1w_2w_3 : w_1 \in L_1, w_2 \in L_2, w_3 \in L_3\}.$$ We denote the common value by $L_1L_2L_3$.
The "zero" element for concatenation is the empty language $\emptyset$, which satisfies $L\emptyset = \emptyset L = \emptyset$. The "one" element for concatenation is the language consisting of only the empty word $\{\epsilon\}$, which satisfies $L\{\epsilon\} = \{\epsilon\}L = L$.