Suppose you have a friend at a different university

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 the
CSU-Global Guide to Writing and APA Requirements
The three questions you must solve for your friend are:
– How many different ways can 28 runners place in an Olympic qualifying
marathon?
– 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?
– 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?