What is the probabililty if you throw six dice, at least one number will appear exactly once?
I know it involves the inclusion exclusion principle but i'm still confused about how to solve it
Consider Ai to be the set of dice rolls that have number i appearing exactly once.
You want to find $\displaystyle \frac{\left|\begin{array}{c}6\\\bigcup\\i=1\end{ar ray} A_i\right|}{\left|\mbox{The set of all possible dice rolls}\right|}$
Apply the inclusion-exclusion principle to find $\displaystyle \left|\begin{array}{c}6\\\bigcup\\i=1\end{array} A_i\right|$
Inclusion-exclusion principle - Wikipedia, the free encyclopedia