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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 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?Coins and Dice

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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?


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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).

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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?

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5. The Rangahan restaurant offers eight starters, ten main courses and three desserts. How many different 3 course meals are there to choose from?

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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?

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7. Two numbers are chosen randomly from one to ten. How many of all the possible selections have a difference of 3?

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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?

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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]

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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]

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


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?

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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.

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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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