Sum of #s on dice.

Question

Six standard six-sided dice are rolled, and the sum $S$ is calculated. What is the probability that $S × (42 – S ) < 297?$ Express your answer as a common fraction.

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First off can I ONLY just have a HINT to start off because I have no idea how? Then once I get it I can post what I did on another question.

Answer 1

Look at the graph of $y=x(42-x)$ and figure out for what values of $x$ does the graph lie below the horizontal line $y=297$. This will allow you to rewrite the condition $S(42-S)<297$ in a simpler way.

Answer 2

Hint 1: The sum can range in $6\le S\le 36$.

Hint 2: Make up the system of inequalities to find possible values of $S$: $$\begin{cases}6\le S\le 36 \\ S(42-S)<297\end{cases} \Rightarrow \begin{cases}6\le S\le 36 \\ S<9 \ \text{or} \ S>33\end{cases} \Rightarrow S=\{6,7,8,34,35,36\}.$$ Hint 3: Find the number of outcomes that give these sums.