Inclusion Exclusion Dice Problem

**morganfor** · August 28th 2009, 04:07 PM

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

**DaRush19** · August 30th 2009, 02:07 AM

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

**pedrosorio** · August 30th 2009, 05:42 AM

Consider Ai to be the set of dice rolls that have number i appearing exactly once.

You want to find $\frac{\left|\begin{array}{c}6\\\bigcup\\i=1\end{ar ray} A_i\right|}{\left|\mbox{The set of all possible dice rolls}\right|}$

Apply the inclusion-exclusion principle to find $\left|\begin{array}{c}6\\\bigcup\\i=1\end{array} A_i\right|$

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