# Thread: Inclusion Exclusion Dice Problem

1. ## Inclusion Exclusion Dice Problem

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

2. Did you find an answer to this? I'm stuck on the same question

3. 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