Total number of outcomes in probability

Every probability is a fraction: $\frac{\text{favorable outcomes}}{\text{total outcomes}}$.
The total number of outcomes is the denominator — it counts all the results that could possibly happen.

For a single choice, the total is simply how many options there are.
A bag with $5$ red, $3$ blue, and $2$ green marbles has $5 + 3 + 2 = 10$ possible outcomes for one draw.

When something happens in stages, multiply the number of choices at each stage.
If the item is replaced each time, the count stays the same: drawing $3$ balls from $50$ with replacement gives $50 \times 50 \times 50$ outcomes.
If it is not replaced, the count drops each time: drawing $3$ balls from $15$ gives $15 \times 14 \times 13$.

For a two-way event repeated several times, the total doubles each time.
One coin toss has $2$ outcomes, two tosses have $2 \times 2 = 4$, and $n$ tosses have $2^n$.

When the outcomes come in separate groups, add the group sizes to get the total.
If a library has $580$, $1350$, and $2680$ books in three sections, the total number of books to choose from is their sum, $4610$.

A jar holds $4$ red, $3$ blue, and $2$ green candies. How many possible outcomes are there when you draw one candy?
Count every candy you could draw: $4 + 3 + 2 = 9$.
So there are $9$ total outcomes.

Two cards are drawn one after another from a set of $12$ cards, without replacement. How many outcomes are possible if the order matters?
The first card can be any of $12$, and the second any of the remaining $11$.
So the total is $12 \times 11 = 132$.

A standard six-sided die is rolled twice. How many total outcomes are there?
Each roll has $6$ possible results, and the rolls are independent.
So the total is $6 \times 6 = 36$.