probability rolling a dice 5 times I can't solve this problem:
What is the probability that, when rolling a dice 5 times, the number of times when you get a 1 or 2 is greater than the number of times when you get a 6.
any help?

It can be solved using ordinary generating functions:
Since there are three groups of numbers of our interest, take three formal variables for the ogf.
Let $x$ indicate 1 or 2, $z$ indicate a 6, and $y$ the other three numbers of the dice.
Hence, the required ogf is:
\begin{align*}
\left(2\, x + 3\, y + z\right)^5  
\end{align*}
We need to consider cases with the variables, though.
Grouping the coefficients for which the degree of $x$ $>$ the degree of $y$, the sum turns out to be $4602$, and the 
probability is 
\begin{align*}
  \mathbb{P} &= \frac{4602}{6^5} = \frac{767}{1296} \approx 0.5918209876543
\end{align*}
