Let's work through the questions in the image step-by-step.

5) How many sundaes are possible?

• Choices for containers: Cup, Sugar Cone, Waffle Cone (3 choices).
• Choices for ice cream: Vanilla, Chocolate (2 choices).
• Choices for toppings: Sprinkles, Hot Fudge, Crushed Cookies (3 choices).

The total number of sundaes possible is the product of the number of choices in each category: $3 \, (\text{containers}) \times 2 \, (\text{ice creams}) \times 3 \, (\text{toppings}) = 18 \, \text{possible sundaes}.$

So, the answer is 18.

6) What is the probability of a waffle cone, vanilla ice cream, and sprinkles sundae?

To find this probability, we need to consider the total number of sundaes possible, which we calculated as 18.

Now, let’s look at the specific combination:

• 1 choice for the waffle cone.
• 1 choice for vanilla ice cream.
• 1 choice for sprinkles.

Since this is one specific combination out of 18 total possibilities, the probability is: $\frac{1}{18}.$

7) What is the probability that your best friend will order not a cup, vanilla ice cream, and crushed cookies?

We will again use the total number of sundaes, which is 18.

Now, consider the conditions:

• Not a cup: This leaves two options (sugar cone, waffle cone).
• Vanilla ice cream: 1 choice.
• Crushed cookies: 1 choice.

The number of favorable outcomes is: $2 \, (\text{containers other than a cup}) \times 1 \, (\text{vanilla ice cream}) \times 1 \, (\text{crushed cookies}) = 2.$

Thus, the probability is: $\frac{2}{18} = \frac{1}{9}.$

Would you like a deeper explanation for any of these answers?

Here are 5 related questions to expand on this:

1. How would the total number of sundaes change if a third ice cream flavor was added?
2. What is the probability of choosing a sugar cone, chocolate ice cream, and hot fudge?
3. What is the probability of choosing a cup, any ice cream flavor, and sprinkles?
4. How would the probability of choosing a sundae with no toppings be calculated?
5. What is the probability of picking vanilla ice cream regardless of the other choices?

Tip: In probability, always double-check whether events are independent before multiplying them!