# 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 6: standard combinations questions.

For each of the questions in this level the order of the items picked, selected or dealt does not matter.

 1. It is time for Jasmin to pack for her holiday in the countryside. She loves to read while she is on holiday but only has a limited amount of space for books in her bag. Jasmin has six books to choose from and will pack only two of them. How many different ways can she do this? 2. You have seven friends and you can pick three of them to join you on a trip to the theatre. How many ways are there of picking the three friends? 3. A shop sells nine different types of fruit. I buy two different pieces of fruit for my lunch. How many different ways can I choose? 4. From a pack of nine cards, numbered 1 to 9, a player is dealt three cards. How many different hands (set of three cards) could the player have been dealt? 5. There are 14 players in the Transum Football Club squad. Only 11 of them are required for the start of a match. How many ways can 11 be selected from 14? 6. How many ways are there of selecting two children from a group of two girls and three boys such that at least one of the chosen children is a boy? 7. The chances of winning The UK National Lottery are quite slim. Six numbers are drawn at random from the set of integers between 1 and 49? How many different groups of six numbers is it possible to choose? 8. Out of six consonants and three vowels, how many possible sets of two consonants and two vowels can be formed?
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This is Systematic Listing Strategies level 6. You can also try:
Level 1 Level 2 Level 3 Level 4 Level 5 Level 7

## 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.

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This spectacular magic trick never fails to amaze people of all ages assuming they can add and subtract very simple numbers. The mathematics comes in finding out how the trick works.

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## 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.

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## 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:

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© Transum Mathematics :: This activity can be found online at:
www.transum.org/Maths/Exercise/Listing/Default.asp?Level=6

## Description of Levels

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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

The video above is from Jackson Walker.

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.

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