The question asks how many branches a tree diagram would have to show all the ways two ten-sided dice could be rolled. Let's solve this step-by-step.

Step 1: Understand the problem

• A ten-sided die has 10 possible outcomes (numbers 1 to 10).
• Two dice are being rolled, so we need to consider all possible combinations of outcomes for both dice.
• A tree diagram would show each possible result from rolling the first die and, for each of those results, all the possible outcomes of rolling the second die.

Step 2: Total number of branches

• The first die has 10 possible outcomes.
• For each outcome of the first die, there are 10 possible outcomes for the second die.
• Thus, the total number of branches is:

$\text{Total branches} = 10 \times 10 = 100$

Final Answer:

The tree diagram would have 100 branches.

Would you like further explanation or assistance with similar problems?

5 Related Questions:

1. What is the formula for finding the total outcomes when rolling multiple dice with different sides?
2. How many branches would there be for three ten-sided dice?
3. Can this be represented using a grid instead of a tree diagram?
4. How does the number of branches change if the dice are six-sided instead?
5. What are the probabilities of rolling specific sums with two ten-sided dice?

Tip:

When calculating combinations or outcomes, always consider how many choices are available at each step, then multiply them for the total!