# Systematic Listing Strategies

## Apply systematic listing strategies to find the number of combinations and permutations of choices.

##### Level 1Level 2Level 3Level 4Level 5Level 6Level 7Exam-StyleDescriptionHelpMore...

This is level 7: mixed combinatorics questions.

 1. Two coins are tossed and a dice rolled all at the same time. How many different possible outcomes are there? 2. How many ways can a group of eight children (six girls and two boys) sit on a row of eight chairs if the two boys are to sit next to each other? 3. Each morning when Elaine leaves home for work she can choose whether or not to take with her an umbrella, a pair of sunglasses and a hat. How many different possibilities are there for her choice (including choosing none and all three items). 4. Windthrup is with four other people at a bus stop. How many ways can they all stand in a line without Windthrup being at the back of the queue? 5. The Rangahan restaurant offers eight starters, ten main courses and three desserts. How many different 3 course meals are there to choose from? 6. A green grocer shop sells eleven different types of fruit. I buy two different pieces of fruit for my picnic. How many different ways can I choose? 7. Two numbers are chosen randomly from one to ten. How many of all the possible selections have a difference of 3? 8. There are 67 students in Year 13 and 74 students in Year 12 at Mathsi School. Two representatives are chosen from each year group. In how many different ways can this be done? 9. Given an unlimited supply of 50p, £1 and £2 coins, in how many different ways is it possible to make a sum of £100? [This question is from a UKMT Senior Maths Challenge paper] 10. A bracelet is to be made by threading four identical red beads and four identical yellow beads onto a hoop. How many different bracelets can be made? [This question is from the Nov 2007 UKMT Senior Maths Challenge paper]
Check

This is Systematic Listing Strategies level 7. You can also try:
Level 1 Level 2 Level 3 Level 4 Level 5 Level 6

## Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

## More Activities:

Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?

Comment recorded on the 6 May 'Starter of the Day' page by Natalie, London:

"I am thankful for providing such wonderful starters. They are of immence help and the students enjoy them very much. These starters have saved my time and have made my lessons enjoyable."

Comment recorded on the 19 June 'Starter of the Day' page by Nikki Jordan, Braunton School, Devon:

"Excellent. Thank you very much for a fabulous set of starters. I use the 'weekenders' if the daily ones are not quite what I want. Brilliant and much appreciated."

Each month a newsletter is published containing details of the new additions to the Transum website and a new puzzle of the month.

The newsletter is then duplicated as a podcast which is available on the major delivery networks. You can listen to the podcast while you are commuting, exercising or relaxing.

Transum breaking news is available on Twitter @Transum and if that's not enough there is also a Transum Facebook page.

#### Online Logo

An opportunity for students to write a computer program. There is nothing to download, all of the interaction takes place in the browser. Great for understanding angles and the properties of shapes.

There are answers to this exercise but they are available in this space to teachers, tutors and parents who have logged in to their Transum subscription on this computer.

A Transum subscription unlocks the answers to the online exercises, quizzes and puzzles. It also provides the teacher with access to quality external links on each of the Transum Topic pages and the facility to add to the collection themselves.

Subscribers can manage class lists, lesson plans and assessment data in the Class Admin application and have access to reports of the Transum Trophies earned by class members.

Subscribe

## Go Maths

Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school.

## Maths Map

Are you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.

## Teachers

If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows:

Alternatively, if you use Google Classroom, all you have to do is click on the green icon below in order to add this activity to one of your classes.

It may be worth remembering that if Transum.org should go offline for whatever reason, there is a mirror site at Transum.info that contains most of the resources that are available here on Transum.org.

When planning to use technology in your lesson always have a plan B!

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.

For Students:

For All:

Scan the QR code below to visit the online version of this activity.

https://www.Transum.org/go/?Num=712

## Description of Levels

Close

Level 1 - Practical listing activities

Level 2 - Find missing items and errors

Level 3 - The product rule for counting

Level 4 - Find the number of arrangements

Level 5 - Standard permutation questions

Level 6 - Standard combinations questions

Level 7 - Mixed combinatorics questions

Exam Style questions are in the style of GCSE or IB/A-level exam paper questions and worked solutions are available for Transum subscribers.

More on this topic including lesson Starters, visual aids and investigations.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

## Example

You may also want to use a calculator to check your working. See Calculator Workout skill 14.

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

Close