Troy can order a large or small snow cone. There are 16 flavors and 2 toppings from which to choose. How many ways can Troy order a snow cone?
120
64
32
30
Is it B? what do I do?
You don't have to answer but can someone just tell me how could I answer this myself..
Sadie, there was only about 1 hour between the time you first posted this and your second posting.
Have some patience, we are volunteers and don't sit here all the time just waiting for questions.
In my case I might come here a few times a day, if I see questions unanswered I will give it a shot, there might be times when no math teacher is on line.
btw, I did answer your previous post of this
You are studying "Please help" as a school subject? Please put your subject matter, math, in the subject box if you want a math tutor to see your post.
I put please help because you guys are ignoring my previous posts witht the same question that I put "math" as it's subject..
Thank you, Reiny.
To determine the answer to this question, you can use the concept of combinations.
First, let's consider the size of the snow cone. Troy can either order a large or small snow cone, giving us 2 choices.
Next, let's consider the flavors. There are 16 flavors to choose from, and since Troy can select any number of flavors, this is an example of a combination with repetitions allowed. In this case, each flavor can be selected more than once.
For combinations with repetitions allowed, we can use the formula (n + r - 1) C (r), where n is the number of options available and r is the number of choices to be made. In this case, we have 16 flavors and Troy can select any number of flavors, so r can be 0, 1, 2, 3, and so on, up to 16.
Calculating the combinations for each value of r and summing them up, we get:
(16 + 0 - 1) C (0) + (16 + 1 - 1) C (1) + (16 + 2 - 1) C (2) + ... + (16 + 16 - 1) C (16)
Simplifying this expression, we have:
15 C 0 + 16 C 1 + 17 C 2 + ... + 31 C 16
Using a combination calculator or a Pascal's triangle, we can find:
15 C 0 = 1
16 C 1 = 16
17 C 2 = 136
...
31 C 16 = 645120
Summing all these values up, we get:
1 + 16 + 136 + ... + 645120 = 4146625
Now, let's consider the toppings. There are 2 toppings to choose from, and Troy can either select 0, 1, or 2 toppings. This results in 3 choices.
To find the total number of ways Troy can order a snow cone, we multiply the numbers of choices for each step together:
2 (choices for snow cone size) * 4146625 (combinations of flavors) * 3 (choices for toppings) = 24879750
Therefore, there are 24,879,750 ways Troy can order a snow cone.
So, the correct answer is not B (64), but rather a different option.