Applying Counting Principles

Suppose you have a friend at a different university who is taking a similar math course to one you are taking. He is having problems understanding the subtle differences between permutations and combinations, as well as the accompanying formulas nCr and nPr. Also, he does not understand the Fundamental Counting Principle. In order to help, you pick three questions from your book that deal with these concepts and write him an email.

Directions: 

• For this assignment, you will write a paper that will describe what you would say in an email to this friend. In your “email” you will present the solutions to the three problems below. Show every step of your calculation. Use nCr, nPr and the Fundamental Counting Principle in your email and explain what they mean.
• Include an introduction in your paper/email that gives background on combinations and permutations, provides motivation for learning these ideas, and relates any personal experiences you have with the topic.
• Include a conclusion that summarizes your answers, highlights the main points, and puts things in perspective for your friend.
• Please remember that any written part of your assignments must follow APA format.
  

The three questions you must solve for your friend are:

1. How many different ways can 28 runners place in an Olympic qualifying marathon?
2. If only the eight fastest runners advance to the Olympics; how many different ways can the eight fastest runners be chosen from the whole field of 28 runners?
3. If the runner in first place receives a gold medal, the runner in second place receives a silver medal, and the runner in third place receives a bronze medal, how many different ways can the three medalists be chosen from the entire field of 28 runners?