# Lesson 3: Counting Techniques Printer-friendly version

### Objectives

In this lesson, our goals are to:

• Understand and be able to apply the multiplication principle.
• Understand how to count objects when the objects are sampled with replacement.
• Understand how to count objects when the objects are sampled without replacement.
• Understand and be able to use the permutation formula to count the number of ordered arrangements of n objects taken n at a time.
• Understand and be able to use the permutation formula to count the number of ordered arrangements of n objects taken r at a time.
• Understand and be able to use the combination formula to count the number of unordered subsets of r objects taken from n objects.
• Understand and be able to use the combination formula to count the number of distinguishable permutations of n objects, in which r are of the objects are of one type and nr are of another type.
• Understand and be able to count the number of distinguishable permutations of n objects, when the objects are of more than two types.
• Learn to apply the techniques learned in the lesson to new counting problems.