The given alphabet is
$$\Sigma = \left\{ a, b, c \right\}$$
I am looking for a nondeterministic finite-state machine which accepts the following words:
$$L=\left\{w\in \Sigma^* \mid \exists x\in\Sigma:\left| w \right|_x=0\right\}$$
with $$\left|Q \right| = 4$$ (number of states).
In simple words the machine should accept all words which use a maximum of 2 symbols out of 3 of the alphabet. This exercise should be rather easy but I just don't know how to count the number of different symbols.