Transum Software

Systematic Listing Strategies

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

Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Level 7 Exam-Style Description Help More...

This is level 5: standard permutation questions.

1. How many ways can seven books be ordered on a book shelf?

Book Shelf

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2. Three books are chosen from the seven above and arranged on another shelf. In how many different ways could this happen?

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3. In how many ways can a supermarket manager display five brands of washing powder in three spaces on a shelf?

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4. Six people take part in a one hundred metre sprint. In how many different ways is it possible for the first three prizes to ba awarded assuming there is not a draw?

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5. How many two digit numbers can you make using the digits 1, 2, 3, 4 and 5 without repeating the digits?

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6. In how many different ways can gold, silver and bronze medals be awarded to the winners of a swimming competition if 20 people entered?

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7. The Transum Club membership ID contains three of the digits 0 to 9 followed by a letter A to Z [e.g. 912H]. No ID must have a repeated digit. What is the total number of all the unique IDs?

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8. The Aston Murmur School student registration code contains four of the digits 0 to 9 followed by a letter A to H [e.g. 1387B]. No registration code must have a repeated digit. What is the total number of all the possible codes?

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9. A particular word does not have any repeated letters. There are five thousand and forty different ways of arranging the letters in the word. How many letters are in that word?

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10. A concert consists of three instrumentals chosen from a collection of six possibilities. They are followed by an interval then five songs chosen from seven possible songs. How many different versions of the running order for this concert will there be?

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This is Systematic Listing Strategies level 5. You can also try:
Level 1 Level 2 Level 3 Level 4 Level 6 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 web site contains over a thousand free mathematical activities for teachers and pupils. Click here to go to the main page which links to all of the resources available.

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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 9 October 'Starter of the Day' page by Mr Jones, Wales:

"I think that having a starter of the day helps improve maths in general. My pupils say they love them!!!"

Comment recorded on the 19 October 'Starter of the Day' page by E Pollard, Huddersfield:

"I used this with my bottom set in year 9. To engage them I used their name and favorite football team (or pop group) instead of the school name. For homework, I asked each student to find a definition for the key words they had been given (once they had fun trying to guess the answer) and they presented their findings to the rest of the class the following day. They felt really special because the key words came from their own personal information."

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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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www.transum.org/Maths/Exercise/Listing/Default.asp?Level=5

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.

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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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