options: Make inferences and justify conclusions from sample surveys, experiments, and observational studies.

Summarize, represent, and interpret data on a single count or measurement variable.

Understand and evaluate random processes underlying statistical experiments.

Interpret linear models.

Calculate expected values and use them to solve problems.

Draw informal comparative inferences about two populations.

Develop understanding of statistical variability.

Use random sampling to draw inferences about a population.

Summarize, represent, and interpret data on two categorical and quantitative variables.

Understand independence and conditional probability and use them to interpret data.

Summarize and describe distributions.

Investigate chance processes and develop, use, and evaluate probability models.

Use the rules of probability to compute probabilities of compound events in a uniform probability model.

Investigate patterns of association in bivariate data.

Use probability to evaluate outcomes of decisions.
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:
{"table": [{"_attributes": {"class": ["table", "table-bordered"], "style": "width:30%"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align:center"}, "_value": "1"}, {"_attributes": {"style": "text-align:center"}, "_value": "2"}, {"_attributes": {"style": "text-align:center"}, "_value": "3"}, {"_attributes": {"style": "text-align:center"}, "_value": "4"}, {"_attributes": {"style": "text-align:center"}, "_value": "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: 12