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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 3: the product rule for counting.

1. A small Thai restaurant offers three main courses and two desserts for a lunchtime special. Customers can choose one main course and one dessert. How many different meals is it possible to select?

Correct Wrong

2. An Indian restaurant offers five main courses and five desserts. Customers can choose one main course and one dessert. How many different meals is it possible to select?

Correct Wrong

3. A Chinese restaurant offers four Starters, five main courses and three desserts. Customers can choose one starter, one main course and one dessert. How many different meals is it possible to select?

Correct Wrong

4. If you would like to buy a new Jay Phone you have the choice of eight different colours, three different screen sizes and either 64GB 128GB or 256GB capacity. How many different combinations of colour, screen size and capacity are there?

Correct Wrong

5. There are 13 men and 17 women in a choir. One of the men and one of the women are going to be chosen to make a pair to sing the first song at a concert. Work out the number of different pairs that can be chosen.

Correct Wrong

6. Bradley has a combination lock for his bicycle. He has to set each of the three parts of the lock to a digit between 0 and 9 inclusive [e.g. 517]. How many different ways can Bradley do this?

Correct Wrong

7. Carol Countdown thinks of a three digit number. The first digit is a square number. The second digit is a prime number and the whole number is odd. How many different numbers could carol be thinking of?

Correct Wrong

8. Graham has 9 pairs of shoes, 6 pairs of trousers, 20 shirts and 15 ties. Everyday he wears a different combination of these four things. How many days will this wardrobe last him?

Correct Wrong

9. In the Greasy spoon restaurant there are 32 different meal choices selected from a list of main courses and a list of desserts. If there are twice as many main courses as desserts, how many desserts are there?

Correct Wrong

10. It is decided that one boy and one girl will be chosen from a class to represent the class on the school council. Frieda calculates that there are exactly 143 ways of making that selection. How many pupils are in this class (the answer is less than 40).

Correct Wrong

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


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.

Why am I learning this?

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 1 February 'Starter of the Day' page by Terry Shaw, Beaulieu Convent School:

"Really good site. Lots of good ideas for starters. Use it most of the time in KS3."

Comment recorded on the 28 May 'Starter of the Day' page by L Smith, Colwyn Bay:

"An absolutely brilliant resource. Only recently been discovered but is used daily with all my classes. It is particularly useful when things can be saved for further use. Thank you!"

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Description of Levels



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.

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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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