TITLE: A four sided fair dice is rolled 10 times. What is the probability of two sides being absent and two sides being present?
QUESTION [3 upvotes]: When solving this question

A four sided fair dice is rolled 10 times. What is the probability of two sides being absent and two sides being present? 

I get the result $$\frac{{4 \choose 2} \cdot 2^{10}}{4^{10}}$$ 
yet the official answer is 
$$\frac{{4 \choose 2}(2^{10}-2)}{4^{10}}$$
Anyone who can explain where this $-2$ comes from?

REPLY [5 votes]: You have to exclude the possibility that only one side is present.  Given that two sides have been excluded, there are two ways this could occur.
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