Find the number of parallelograms by finding the number of combinations and applying the principle of counting by multiplication.
After completing this tutorial, you will be able to complete the following:
In this Activity Object, the learner is given a word problem involving finding the number of parallelograms formed when m parallel lines intersect with other n transversal parallel vertical lines. In order to solve this problem, the combination formula and the principle of counting by multiplication will be used.
Combination Formula When the order is not important, you can find the number of selections of r objects from a set of n objects by using the combination formula:
For example, Eleven students put their names in a hat to pick three names for a committee. How many different ways can the three names be selected out of the hat?
Principle of Counting by Multiplication
There are several counting methods, but this Activity Object focuses on the principle of counting by multiplication:
If an event occurs in m ways and another event occurs independently in n ways, then the two events can occur in m × n ways.
If there are shirts for sale in 3 colors (red, blue, and yellow) and come in 4 sizes (small, medium, large, and X-large), how many different shirts are available?
3 × 4 = 12 different shirts
The following key vocabulary terms will be used throughout this Activity Object:
|Approximate Time||20 Minutes|
|Pre-requisite Concepts||principle of counting by multiplication, combination formula|
|Type of Tutorial||Problem Solving & Reasoning|
|Key Vocabulary||combination, counting principle, parallelograms|