Math  /  Discrete

QuestionWhen making an ice cream sundae, you have a choice of 2 types of ice cream flavors; chocolate (C) or vanilla (V); a choice of 4 types of sauces: hot fudge ( HH ), butterscotch (B), strawberry (S), or peanut butter (P); and a choice of 3 types of toppings; whipped cream (W), fruit (F), or nuts ( N ). If you are choosing only one of each, list the sample space in regard to the sundaes (combinations of ice cream flavors, sauces, and toppings) you could pick from.

Studdy Solution

STEP 1

What is this asking? How many different sundaes can we make with two ice cream flavors, four sauces, and three toppings? Watch out! Don't mix up combinations and permutations!
We're just picking one of each, so order doesn't matter.

STEP 2

1. Ice Cream Possibilities
2. Sauce Possibilities
3. Topping Possibilities
4. Total Sundae Combinations

STEP 3

We have 22 delicious ice cream flavors to choose from: **chocolate (C)** and **vanilla (V)**.
That's easy peasy!

STEP 4

We've got 44 scrumptious sauces: **hot fudge (H), butterscotch (B), strawberry (S), and peanut butter (P)**.
Yummy!

STEP 5

And to top it all off, we have 33 fantastic toppings: **whipped cream (W), fruit (F), and nuts (N)**.
This is getting exciting!

STEP 6

To find the **total number of sundae combinations**, we **multiply** the number of choices for each part.
Think of it like this: for *each* ice cream flavor, we can pair it with *each* of the four sauces.
That's 24=82 \cdot 4 = 8 ice cream/sauce combos.
Then, *each* of *those* combos can be paired with *each* of the three toppings.

STEP 7

So, we **multiply** the number of ice cream choices, sauce choices, and topping choices together: 243=242 \cdot 4 \cdot 3 = 24.

STEP 8

We can make a whopping **24 different sundaes**!
That's enough for a whole class party!

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