Exploring permutations

The formula for the number of ways to arrange \(n\) objects is \(n! = n\times(n-1)\times \cdots \times 2 \times 1\). This exercise walks you through the derivation of this formula for a couple of special cases.

A small company has \({{params.part0.list_length}}\) employees: \({{params.part0.list}}\). There are \({{params.part0.list_length}}\) parking spots in a row at the company, none of which are assigned, and each day the employees pull into a random parking spot. That is, all possible orderings of the cars in the row of spots are equally likely.

Part 1

On a given day, what is the probability that the employees park in alphabetical order? (Answer in fraction.)

Answer Section

Please enter a numeric value in.

Part 2

If the alphabetical order has an equal chance of occurring relative to all other possible orderings, how many ways must there be to arrange the five cars?

Answer Section

Please enter a numeric value.

Part 3

Now consider a sample of \({{ params.part3.num1 }}\) employees instead. How many possible ways are there to order these \({{ params.part3.num2 }}\) employees’ cars?

Answer Section

Please enter a numeric value.

Attribution

Problem is from the OpenIntro Statistics textbook, licensed under the CC-BY 4.0 license.