20.1: Motivation
You probably learned to count before you even started kindergarten. But efficiently counting large collections can be difficult!
- How many different ways can you choose your winning numbers for the lottery?
- How many different possible seating charts could be made for the students in this course in the assigned classroom?
- How many different ways are there for you to choose courses to satisfy your degree requirements?
- How many bijections between the sets \(\{0,1,2,3,4,5\}\) and \(\{a,b,c,d,e,f\}\) exist?
- How many total orders on the set \(\{0,1,2,3,4,5\}\) exist?
- How many partial orders on the set \(\{0,1,2,3,4,5\}\) exist?