Assignment 7 Problem Solving Strategies

Counting

We have learned the following formula for permutations of n objects in k ways as follows:

The goal will be to explain why this formula is correct.

Part 1: Suppose you have 12 different candy bars, and you want to pick 5 of them. How many different stacks of 5 candy bars can you make? Explain how this relates to P(12,5).

Part 2: What does 12! count? What does 7! count? Explain.

Part 3: Why does it make sense to divide 12! by 7! in this case?

Part 4: Can this formula work for any n,k you choose? Or are certain values not possible?

Graph Theory Intro

*Consider drawing a picture to think about these problems*

If a group of 10 friends on social media messaged the other members in their group, how many messages took place?

Explain how this problem relates to graph theory.

Inductive Reasoning

Consider the following relation:

See if this relation holds true for the following: n = 4, n=6

Use mathematical induction to show that this equality will always hold.

Sequences and Recursion

Consider the sequence 5, 9, 13, 17, 21 with

Part 1: Give a recursive definition for the sequence.

Part 2: Is 2013 in the sequence? How do you know?

Part 3: Find the following sum. Explain how you got your solution.