A vending machine sells 2 types of drink (cola, lemonade) and 3 types of snack (crisps, chocolate bar, biscuits). A customer buys one drink and one snack. List all the different drink-and-snack combinations that the customer could buy.
(Total for Question 1 is 2 marks)
2
Tom flips a fair coin (Heads, Tails) and spins a fair spinner with three equal sections labelled X, Y and Z. List all the possible outcomes.
(Total for Question 2 is 2 marks)
3
Using the digits 2, 5 and 8, list all the two-digit numbers that can be made. Each digit can be used only once in each number.
(Total for Question 3 is 2 marks)
4
Jamila lists the outcomes of rolling two fair coins as: HH, HT, HH, TT. Give one reason why Jamila's list is not a correct systematic list of all the outcomes.
(Total for Question 4 is 1 mark)
5
A sandwich shop makes rolls using one type of bread (white or brown) and one filling (cheese, ham or tuna).
(a)List all the different rolls that could be made.(2)
(b)Write down the total number of different rolls possible.(1)
(Total for Question 5 is 3 marks)
6
Two fair spinners, each with sections numbered 1, 2, 3 and 4, are spun. The two numbers are added together to give a total.
(a)Complete the sample space diagram to show all 16 possible totals.(2)
(b)Use your diagram to find the probability that the total is 5.(2)
(Total for Question 6 is 4 marks)
7
A locker code uses 2 different digits chosen from 1, 2, 3 and 4. No digit is repeated in a code.
(a)List all the possible codes.(2)
(b)Write down the total number of different codes possible.(1)
(Total for Question 7 is 3 marks)
8
A school uniform shop sells jumpers in 3 colours (navy, grey, black) and trousers in 2 colours (black, grey). A pupil buys one jumper and one pair of trousers.
(a)List all the different jumper-and-trousers combinations possible.(2)
(b)Ahmed says you do not need to list every combination to find the total number possible. Use multiplication to work out the total number of combinations.(2)
(Total for Question 8 is 4 marks)
9
A cafe sells sandwiches with a choice of 2 types of bread (white, brown) and 4 types of filling (cheese, ham, egg, tuna). A table showing some of the possible combinations has been started below, but is not yet complete.
(a)Complete the table to show all 8 possible bread-and-filling combinations.(2)
(b)Write down the total number of different sandwiches possible.(1)
(Total for Question 9 is 3 marks)
10
Aisha, Ben and Chidi stand in a line to have their photograph taken. List all the different possible orders in which the three friends can stand, and write down the total number of arrangements.
(Total for Question 10 is 3 marks)
11
A dessert cart sells ice cream in 4 flavours and 3 toppings. A customer chooses one flavour and one topping. Without listing them, work out the total number of different one-scoop, one-topping ice creams possible.
(Total for Question 11 is 2 marks)
12
A restaurant's set menu offers a choice of 3 starters, 4 main courses and 2 desserts. A customer chooses one of each course. Work out the total number of different three-course meals possible.
(Total for Question 12 is 2 marks)
13
A gym locker code is made from 2 digits. Each digit is chosen from 1 to 9 and digits may be repeated. Work out the total number of different codes possible.
(Total for Question 13 is 2 marks)
14
A fencing company offers fence panels in 3 styles (lattice, picket, plain) and paint in 2 colours (green, brown). A customer chooses one style and one colour.
(a)List, or draw a table to show, all the different style-and-colour combinations possible.(2)
(b)A combination is chosen at random from all the possibilities in part (a). Find the probability that it is the picket style painted brown.(2)
(Total for Question 14 is 4 marks)
15
Two ordinary fair 6-sided dice are rolled together and the two scores are added to give a total.
(a)Complete the sample space diagram to show all 36 possible totals.(2)
(b)Use your diagram to find the probability that the total is greater than 8.(2)
(Total for Question 15 is 4 marks)
16
A padlock code is made from 3 digits. Each digit is chosen from 0 to 9 and digits may be repeated. Work out the total number of different codes possible.
(Total for Question 16 is 2 marks)
17
Nadia wants to make exactly 30p using only 20p, 10p and 5p coins. She may use more than one of each coin, or none of some of them. List all the different ways she could make exactly 30p, showing the number of each coin used each time.
(Total for Question 17 is 3 marks)
18
A computer password is 3 letters long, using 3 different letters chosen from the 5 letters A, B, C, D and E. The order of the letters matters and no letter is repeated. Without listing them, work out the total number of different passwords possible.
(Total for Question 18 is 2 marks)
19
Farah has 4 different books: a novel (N), a biography (B), a comic (C) and a dictionary (D). She chooses 2 of the books and places them in order on a shelf, so the order matters (for example, NB is different from BN). List all the different possible arrangements of 2 books, and state the total number of arrangements.
(Total for Question 19 is 3 marks)
20
A meal deal lets a customer choose 1 of 3 breads, 1 of 4 fillings and 1 of 2 sauces. The chilli sauce cannot be chosen together with the tuna filling. Work out the total number of different meal deals possible.
(Total for Question 20 is 3 marks)
Mark scheme · 2.3 Systematic Listing
Question 1
B1 systematic list or table shown, at least 4 correct combinations
B1 all 6 combinations listed with no repeats or omissions
Answer: cola+crisps, cola+chocolate bar, cola+biscuits, lemonade+crisps, lemonade+chocolate bar, lemonade+biscuits (6 combinations)
Question 2
B1 systematic list or table shown, at least 4 correct outcomes
B1 all 6 outcomes listed with no repeats or omissions
Answer: HX, HY, HZ, TX, TY, TZ (6 outcomes)
Question 3
B1 systematic list shown, at least 4 correct numbers
B1 all 6 numbers correct with no repeats or omissions: 25, 28, 52, 58, 82, 85
Answer: 25, 28, 52, 58, 82, 85 (6 numbers)
Question 4
B1 correct reason oe, e.g. HH has been written twice / TH has been left out
Answer: HH is repeated and TH is missing (any valid correct reason about a repeat or omission)
Question 5
(a) B1 systematic list or table shown, at least 4 correct rolls
(a) B1 all 6 rolls correct with no repeats or omissions