few_shots: Example:
Problem/activity:
You’re mixing ingredients for cookies. The recipe says to combine 6 tablespoons, or ¾ stick, of butter with 1 cup of sugar. You accidentally mix in a whole stick of butter (8 tablespoons) with the cup of sugar. How can you fix this?


Standard options: 
A. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”
B. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
C. Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” (Expectations for unit rates in this grade are limited to non-complex fractions.)


Your response, in json format:
{
  "explanation": "This problem solves a real-world problem involving mixing ingredients for cookies. A student doing this problem would need to reason about equivalent ratios of butter amounts to sugar amounts.",
  "answer": "B"
}

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: fl_problem_000972

6
options: Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.

Use permutations and combinations to compute probabilities of compound events and solve problems.

Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model.

Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model.
problem_activity: Problem 1
Using the digits 1, 2, and 3, write an expression to answer the following questions
How many different three-digit numbers can you make when you can use each digit more than once?
How many different three-digit numbers can you make when you can only use each digit once?
Problem 2
Your phone requires you to use five numbers for the code, but you only can use numbers 1-5 for the code.
The first combination you come up with is:
| 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|
You then realize how "insecure" this number might be since anyone could guess it. Figuring this out you wonder, "How many possibilities are there for combinations if I only use each number once?"
Problem 3
You change the phone settings so that you only need a three-digit code to open the lock.
This means you have 5 numbers to choose from and 3 positions to put those numbers in, which is represented by
$$_5P_3$$
. How many different combinations can you get if you have three positions and a choice of five numbers with no repetition?


correct_option_index: 1