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Lesson: Counting With Repetition Where Order Does Not Matter Mathematics

In this lesson, we will learn how to use combinations to count with repetition where order does not matter.

Lesson Plan

Students will be able to

solve problems in which we need to count with repetition and in which we treat different orderings of the same collection as equivalent (e.g., ),
use double counting techniques to think about problems in combinatorics and mathematics more generally.

Lesson Explainer

Lesson Worksheet

Q1:

A magician wants to hide 4 identical balls in 16 boxes. More than one ball can be placed in a box. In how many ways can the balls be hidden?

Q2:

Twenty passengers get on an airport shuttle. The shuttle route includes six hotels, and each passenger gets off the shuttle at his/her hotel. The driver records how many passengers leave the shuttle at each hotel. How many different possibilities exist?

Q3:

How many integer solutions are there for the equation , given that , , and ?