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 ( 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.
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Separate the elements of the sample space with commas.
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 forget to consider *all* the possible combinations!
STEP 2
1. Calculate the number of choices.
2. List all the sundaes.
STEP 3
We have ice cream flavors, sauces, and toppings.
Since we're picking one of each, we **multiply** the number of choices together.
This is because each ice cream choice can be paired with *any* of the sauce choices, and *each* of those pairs can be matched with *any* of the topping choices.
STEP 4
So, the total number of different sundaes is .
That's a lot of sundaes!
STEP 5
Let's use the abbreviations given in the problem: C for chocolate, V for vanilla, H for hot fudge, B for butterscotch, S for strawberry, P for peanut butter, W for whipped cream, F for fruit, and N for nuts.
STEP 6
Now, we systematically list all combinations.
We'll start with chocolate ice cream (C), go through all the sauces, and for each sauce, list all the toppings.
STEP 7
Chocolate Ice Cream (C): CHW, CHF, CHN, CBW, CBF, CBN, CSW, CSF, CSN, CPW, CPF, CPN
STEP 8
Vanilla Ice Cream (V): VHW, VHF, VHN, VBW, VBF, VBN, VSW, VSF, VSN, VPW, VPF, VPN
STEP 9
The sample space of sundaes is CHW, CHF, CHN, CBW, CBF, CBN, CSW, CSF, CSN, CPW, CPF, CPN, VHW, VHF, VHN, VBW, VBF, VBN, VSW, VSF, VSN, VPW, VPF, VPN.
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