# Expected number of different faces in multiple die roles

I roll 6 6-sided regular dice. What is the expected number of unique up-facing sides I will find among those dice?

The easiest way is to calculate the probability you will see one particular number, then use the linearity of expectation to multiply by $6$. What is the chance you see a $1$ with six dice?
• @DoubleAA: The chance that you see a $1$ is not $1$. You can certainly have rolls like $222222$ that don't have any $1$'s. The expected number of $1$'s is $1$, but that counts $111111$ as $6$. We want to count it as only yes-1 roll that has a one. So what is the chance you see a $1$ with six dice? – Ross Millikan Apr 17 '13 at 20:18