Systematic Listing worksheet
8 GCSE practice questions with answers, free to print. Every sheet is generated, so you can make a fresh one whenever you need it.
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3 marks
Dev is choosing one filling and one type of bread at a sandwich shop.
The filling can be chicken, cheese or falafel.
The type of bread can be white or brown.
(a)List all the possible combinations he could choose.
(b)Dev decides to add a sauce as well. There are 6 different sauces to choose from.
How many different combinations are possible now?
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3 marks
Here are three cards. Each card has one digit written on it.
2 3 6 (a)Each card is used once to make a three-digit number.
Write down all the three-digit numbers that can be made, starting with the smallest.
(b)A different set of 3 cards is used, each showing a different digit. This time a card may be used more than once, so a digit can be repeated.
How many different three-digit numbers can be made from that set?
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4 marks
Rosa, Sam, Tariq and Uma are in a group.
(a)Two of them are chosen to run the stall.
List all the possible pairs that could be chosen.
(b)A larger group of 6 people is asked instead. One of them is chosen to be manager and a different one is chosen to be assistant manager.
Work out how many different ways this can be done.
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4 marks
There are 9 teams in a school football league.
(a)Each team plays every other team once.
Work out the total number of matches played.
(b)The next season, each team plays every other team twice: once at home and once away.
Work out the total number of matches played that season.
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3 marks
Amara is choosing one sandwich and one drink at a café.
The sandwich can be cheese, tuna or egg.
The drink can be water or orange juice.
(a)List all the possible combinations she could choose.
(b)Amara decides to add a piece of fruit as well. There are 6 different pieces of fruit to choose from.
How many different combinations are possible now?
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3 marks
Here are three number cards.
4 7 8 (a)Each card is used once to make a three-digit number.
Write down all the three-digit numbers that can be made, starting with the smallest.
(b)A different set of 3 cards is used, each showing a different digit. This time a card may be used more than once, so a digit can be repeated.
How many different three-digit numbers can be made from that set?
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4 marks
Alina, Bruno, Celia and Dmitri are in a group.
(a)Two of them are chosen to judge the competition.
List all the possible pairs that could be chosen.
(b)A larger group of 5 people is asked instead. One of them is chosen to be chief judge and a different one is chosen to be second judge.
Calculate how many different ways this can be done.
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4 marks
There are 9 teams in a chess club league.
(a)Each team plays every other team once.
Work out the total number of matches played.
(b)The next season, each team plays every other team twice: once at home and once away.
Work out the total number of matches played that season.
Answers
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(a) chicken and white, chicken and brown, cheese and white, cheese and brown, falafel and white, falafel and brown
(b) \(36\) -
(a) \(236,\ 263,\ 326,\ 362,\ 623,\ 632\)
(b) \(27\) -
(a) Rosa and Sam, Rosa and Tariq, Rosa and Uma, Sam and Tariq, Sam and Uma, Tariq and Uma
(b) \(30\) -
(a) \(36\)
(b) \(72\) -
(a) cheese and water, cheese and orange juice, tuna and water, tuna and orange juice, egg and water, egg and orange juice
(b) \(36\) -
(a) \(478,\ 487,\ 748,\ 784,\ 847,\ 874\)
(b) \(27\) -
(a) Alina and Bruno, Alina and Celia, Alina and Dmitri, Bruno and Celia, Bruno and Dmitri, Celia and Dmitri
(b) \(20\) -
(a) \(36\)
(b) \(72\)