QuestionWhen making an ice cream sundae, you have a choice of 2 types of ice cream flavors: chocolate ( ) or vanilla (V): a choice of 4 types of sauces: hot fudge (H), 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, picking one of each?
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 delicious ice cream flavors to choose from: **chocolate** () and **vanilla** ().
So, we have options for our ice cream base.
STEP 4
We're drowning in choices with scrumptious sauces: **hot fudge** (), **butterscotch** (), **strawberry** (), and **peanut butter** ().
That's saucy options!
STEP 5
To top it all off (literally!), we've got fantastic toppings: **whipped cream** (), **fruit** (), and **nuts** ().
That gives us topping choices.
STEP 6
To find the **total number of sundae combinations**, we **multiply** the number of choices for each part.
It's like branching paths – each ice cream choice leads to all the sauce choices, and each of *those* branches out to all the topping choices!
STEP 7
So, we **multiply**: (ice cream flavors) (sauces) (toppings).
STEP 8
STEP 9
That's a whopping ** different sundae combinations**!
Talk about options!
STEP 10
There are possible sundaes we can create!
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