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Exercise 25

Avg difficulty 3.0

Exploring permutations. The formula for the number of ways to arrange nn objects is n!=n×(n−1)×⋯×2×1n!=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 five employees: Anna, Ben, Carl, Damian, and Eddy. There are five 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.

  1. On a given day, what is the probability that the employees park in alphabetical order?

  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?

  3. Now consider a sample of 8 employees instead. How many possible ways are there to order these 8 employees’ cars?

Diez, Barr & Çetinkaya-Rundel, OpenIntro Statistics, Distributions of random variables, End-of-Chapter Exercises, Exercise 25

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Adapted from OpenIntro Statistics © 2019 David Diez, Mine Çetinkaya-Rundel & Christopher D. Barr. Licensed under CC BY-SA 3.0. Source: OpenIntro Statistics. Imported at revision fee2509.