Given are three 6 sided dice, which we throw at the same time.
The outcome of the throw is given by the triple $(x,y,z)$. I want to know how many combinations have at least one of the dice with a $2$ showing up.
How can I count them without writing down every possible combination $\{(2,1,1),(2,2,1),..\}$? Any well known formula for this kind of counting problems?
There are $6 \times 6 \times 6 = 216$ possible outcomes. The number of outcomes where $2$ does not appear at all is $5 \times 5 \times 5 = 125$.
The number of outcomes where $2$ appears at least once is $216 - 125 = 91$.