The topic Combinatorics involves counting and ordering as well as exploring arrangements, patterns, symmetry and other methods to generalise and predict outcomes. The consideration of the expansion of \((x+y)^n\) where \(n\) is a positive integer, draws together aspects of number theory and probability theory.
A knowledge of combinatorics is useful when considering situations and solving problems involving counting, sorting and arranging. Efficient counting methods have many applications and are used in the study of probability.
The study of combinatorics is important in developing students’ ability to generalise situations, to explore patterns and to ensure the consideration of all outcomes in situations such as the placement of people or objects, setting-up of surveys, jury or committee selection and design.
The diagnostic quiz for Permutations and Combinations has been designed for a quick little revision quiz for the whole Permutations and Combinations topic. Each sub topic of Permutations and Combinations will be covered in the diagnostic quiz.
How to test yourself
Download Quiz The best practice is to use a pen and paper. Use the Download Quiz button to print out the quiz and print it out. There will be plenty of room for working so complete the questions on the paper. This is how the school will give it to you so practice this was as well. You will need to submit your responses online after the quiz is finished but we highly recommend practicing by downloading the quiz.
Complete online If you want to work through the diagnostic quiz "live", click the complete online button. This will give you the questions on the computer screen and you can work through the problem on a sheet of paper. Instantly, you can view the answer and submit your answers.
In both testing cases, you will need to submit your answers online for diagnostics. While both options are available, we recommend you put yourself in the "testing environment" by printing out the quiz.
Why do a Diagnostic Quiz?
Test Understanding - If you have completed the entire topic at school, run through the diagnostic to make sure that you have not forgotton anything
Revision / Test Preparation - The best way to identify which areas to focus on for an upcoming test or school quiz. If you are struggling in a particular subtopic in Permutations and Combinations, the diagnostic quiz will pick this up. This means that you can then go back to the topic quizzes and do additional practice in the right area.