Permutations, Combinations and the Fundamental Counting Principle

Please help me design a mystery, story, or activity that uses what you have learned about permutations and combinations in this module. The number of questions required is up to you, although the suggested number of questions is 5 to 10.

The mystery, story, or activity must include problems that require the understanding of the following concepts or procedures to solve:

• the fundamental counting principle
• factorial notation (e.g., simplifying factorial expressions with numerators and denominators, solving equations involving factorials)
• use of graphic organizers (e.g., tree diagram or using blanks)
• calculating the number of permutations (e.g., permutations where there are some restrictions, permutations where two or more elements are identical)
• the difference between combinations and permutations
• calculating the number of combinations
• probability and permutations, or probability and combinations

For each problem in the mystery, story, or activity, provide a

• complete solution
• description of what mathematical concept(s) the problem relates to permutations, combinations, and fundamental counting principles.