Find the number of ways of posting six letters in three letter boxes such that no letter box remains empty.
This question already has answers here. But my doubt is in the following method.
$$^6C_3\times3^3$$
Is the above method correct or is it just accidental that the answer is coming correct?
Also, shouldn't we be doing $^6P_3$ instead of $^6C_3$ because we would want to arrange the letters too?