Mrs. Mortlock’s Calculator Program

An expert calculator for solving permutation problems, inspired by the classic probability scenario where Mrs. Mortlock uses a calculator program to select students.

Error: N must be greater than or equal to k for non-repetition.

How the total permutations change as the number of selections (k) increases.

What is the “Mrs. Mortlock Uses a Calculator Program” Scenario?

The phrase “Mrs. Mortlock uses a calculator program” originates from a common mathematics problem designed to teach students about probability and permutations. In the classic scenario, a teacher named Mrs. Mortlock randomly selects students from her class to answer a series of questions. This calculator is a tool designed to solve the core mathematical concept of that problem: calculating the number of possible outcomes (permutations) when making a series of selections from a set.

This is a fundamental concept in statistics and computer science. The key question is whether the same student can be picked more than once. If so, we are calculating permutations with repetition. If not, we are calculating permutations without repetition. This tool, the very kind of program Mrs. Mortlock would use, can solve both scenarios instantly.

The Formulas Behind the Program

The calculation depends entirely on whether repetition is allowed. This calculator automatically selects the correct formula based on your choice.

1. Permutations with Repetition

This is used when an item can be selected more than once (e.g., the same student can be chosen for multiple questions). The formula is:

Total Permutations = N^k

2. Permutations without Repetition

This is used when an item cannot be selected more than once (e.g., once a student answers, they are not chosen again). The formula is:

Total Permutations = N! / (N – k)!

Variable	Meaning	Unit	Typical Range
N	The total number of items to choose from.	Unitless (count)	1 to any large integer
k	The number of selections being made.	Unitless (count)	1 to N (or higher with repetition)

For more complex probability calculations, see our Advanced Statistics Guide.

Practical Examples

Example 1: The Classic Mrs. Mortlock Problem

Mrs. Mortlock has 28 students in her class and she asks 5 questions. The program can pick the same student more than once.

• Inputs: N = 28, k = 5, Repetition = Yes
• Formula: N^k
• Result: 28⁵ = 17,210,368 possible ways to select students.

Example 2: No Repeat Students

What if Mrs. Mortlock decides that once a student has answered a question, they won’t be called upon again for the remaining questions?

• Inputs: N = 28, k = 5, Repetition = No
• Formula: N! / (N – k)!
• Result: 28! / (23)! = 28 × 27 × 26 × 25 × 24 = 11,793,600 possible ways.

How to Use This Calculator Program

1. Enter Total Items (N): Input the total number of distinct items you are choosing from. For Mrs. Mortlock, this is her class size of 28.
2. Enter Number of Selections (k): Input how many choices you will make. For the problem, this is 5 questions.
3. Select Repetition: Choose ‘Yes’ if items can be chosen multiple times (the default Mrs. Mortlock scenario) or ‘No’ if each choice must be unique.
4. Interpret Results: The calculator will show the total number of possible permutations, the formula used, a growth table, and a chart to visualize the scale of the outcome. You might find our guide on data visualization helpful here.

Key Factors That Affect the Outcome

• Total Number of Items (N): The most significant factor. A larger set of items creates exponentially more possibilities.
• Number of Selections (k): As you make more selections, the number of permutations grows very quickly, especially with repetition.
• Repetition: Allowing repetition always results in a higher number of possible outcomes compared to not allowing it, provided k > 1.
• Order Matters: This is a permutation calculator, meaning the sequence of selections is important (e.g., [Student A, Student B] is different from [Student B, Student A]).
• Value of (N-k): In non-repetition calculations, as ‘k’ gets closer to ‘N’, the denominator (N-k)! gets smaller, causing the result to increase dramatically.
• Factorial Growth: The factorial function (N!) used in non-repetition formulas grows faster than exponential functions, leading to massive numbers even with moderate inputs. You can learn about this on our page about mathematical functions.

Frequently Asked Questions (FAQ)

Who is Mrs. Mortlock?

Mrs. Mortlock is the fictional subject of a popular math problem used to illustrate permutations with repetition. She is a teacher who uses a program to randomly select students.

What is the difference between a permutation and a combination?

Order. In permutations, the order of selection matters (A, B is different from B, A). In combinations, the order does not matter (A, B is the same as B, A). This is a permutation calculator. Check out our combination vs. permutation explainer for more.

Why does allowing repetition create more outcomes?

Because for each selection (k), you always have the full pool of items (N) to choose from. Without repetition, the pool of available items shrinks with each selection.

What does N! (N Factorial) mean?

It is the product of all positive integers up to N. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120.

Can I use this for things other than students?

Absolutely. It can be used for any scenario where you are selecting items from a set, such as possible password combinations, lottery outcomes, or prize assignments.

Why is the result so large?

Permutations grow at an extremely fast rate. This is known as combinatorial explosion and is a key concept in computer science and statistics. See our post on large number theory.

What happens if k is larger than N without repetition?

It’s impossible. You cannot select more unique items than the total number available. The calculator will show an error in this case.

Is this a real ‘program’ Mrs. Mortlock used?

The ‘program’ is a conceptual part of the story problem. This web page is a real, functional version of what that program would do.