Two fair dice are thrown. Count the outcomes of the sample space that belong to each event…

Step 1. $E_1$. The totals $10$, $11$ and $12$ can be made in $3$, $2$ and $1$ ways. So $E_1$ has $3 + 2 + 1 = 6$ outcomes.

Step 2. $E_2$. The totals $2$, $3$, $5$, $7$ and $11$ can be made in $1$, $2$, $4$, $6$ and $2$ ways. So $E_2$ has $1 + 2 + 4 + 6 + 2 = 15$ outcomes.

Step 3. $E_3$. Each number must be $1$, $3$ or $5$. That gives $3 \times 3 = 9$ outcomes.