Creation of nondeterministic finite-state machine for a word which doesn't contain a certain symbol

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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.