The Product Rule for Counting: Fluency and Exam Drill - Worksheets, Questions and Revision

22 original exam-style questions - 6 pages of questions with a full mark scheme - free printable PDF.

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6.3D The Product Rule for Counting: Fluency and Exam Drill

EDEXCEL 1MA1 · Calculators not allowed · about 65 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
Ayesha has 4 different T-shirts and 3 different skirts.
Work out the number of different outfits she can make by choosing one T-shirt and one skirt.
(Total for Question 1 is 1 mark)
2
A cafe has 3 different starters and 2 different desserts.
Work out the number of different ways Tom can choose one starter and one dessert.
(Total for Question 2 is 1 mark)
3
An ice cream van sells 5 flavours, 3 types of cone and 2 toppings.
Work out the number of different ice creams that can be made by choosing one flavour, one cone and one topping.
(Total for Question 3 is 2 marks)
4
Sam rolls two ordinary six-sided dice, one red and one blue.
Work out the number of different outcomes possible.
(Total for Question 4 is 1 mark)
5
Grace tosses 3 fair coins, one after another.
Work out the number of different sequences of heads and tails possible.
(Total for Question 5 is 2 marks)
6
A PE kit is made from one shirt (4 colours available), one pair of shorts (3 colours available) and one pair of socks (2 colours available).
Work out the number of different PE kits possible.
(Total for Question 6 is 2 marks)
7
A locker code is made from 2 digits, each chosen from 1, 2, 3, 4, 5. Digits may be repeated.
Work out the number of different codes possible.
(Total for Question 7 is 2 marks)
8
A different locker code is made from 2 digits, each chosen from 1, 2, 3, 4, 5, but no digit may be repeated.
Work out the number of different codes possible.
(Total for Question 8 is 2 marks)
9
A gate code is made from 2 letters, each chosen from A, B, C, D. Letters may be repeated.
Work out the number of different gate codes possible.
(Total for Question 9 is 2 marks)
10
Priya has 3 different revision books. She places all 3 books in a row on a shelf.
Work out the number of different orders the books can be placed in.
(Total for Question 10 is 2 marks)
11
A school timetable has 4 different subjects to place into 4 lesson slots on Monday, one subject per slot.
Work out the number of different ways the 4 subjects can be arranged across the 4 slots.
(Total for Question 11 is 3 marks)
12
An access code is made from 1 letter of the alphabet (26 letters) followed by 1 digit (0 to 9).
Work out the number of different access codes possible.
(Total for Question 12 is 2 marks)
13
A sandwich shop offers 3 types of bread, 5 fillings and 4 drinks.
Work out the number of different meal combinations possible by choosing one bread, one filling and one drink.
(Total for Question 13 is 2 marks)
14
A combination lock has 3 dials. Each dial can be set to any digit from 0 to 9, and digits may repeat across dials.
Work out the number of different combinations possible.
(Total for Question 14 is 3 marks)
15
A sports team of 7 players must choose one captain and one different player as vice-captain.
Work out the number of different ways the captain and vice-captain can be chosen.
(Total for Question 15 is 3 marks)
16
A cafe menu has 4 starters, 5 main courses and 3 desserts. One of the starters is tomato soup. A 'complete meal' is one starter, one main course and one dessert, chosen by a customer.
(a)Work out the number of different complete meals possible.(2)
(b)Work out the number of different complete meals that do not include tomato soup.(2)
(Total for Question 16 is 4 marks)
17
A charity club has 8 members. Three different roles, chair, vice-chair and treasurer, are each given to a different member.
(a)Work out the number of different ways the three roles can be given out.(2)
(b)The treasurer role must go to either Kwame or Sophie. Work out the number of different ways the three roles can now be given out.(3)
(Total for Question 17 is 5 marks)
18
A padlock code has 4 digits. Each digit can be any number from 0 to 9.
(a)The digits may be repeated. Work out the number of different codes possible.(2)
(b)The first digit of the code cannot be 0, although the other three digits may still be any digit from 0 to 9 and may repeat. Work out the number of different codes now possible.(3)
(Total for Question 18 is 5 marks)
19
The digits 2, 3, 5, 7 and 8 are each used at most once to form a 3-digit number, so no digit is repeated.
(a)Work out how many different 3-digit numbers can be formed.(2)
(b)Work out how many of these 3-digit numbers are even.(3)
(Total for Question 19 is 5 marks)
20
Raffle tickets are made from one colour, chosen from red, blue, green, yellow and purple, together with a 2-digit number from 00 to 99 (the two digits of the number may repeat, giving 100 different numbers).
Work out the number of different raffle tickets that are not red.
(Total for Question 20 is 3 marks)
21
A student ID is made from 2 letters, each chosen from the 26 letters of the alphabet. Letters may be repeated.
(a)Work out the number of different student IDs possible.(2)
(b)Work out the number of these student IDs that contain at least one letter Z.(3)
(Total for Question 21 is 5 marks)
22
A padlock code has 3 digits. Each digit can be any number from 0 to 9 and digits may repeat, but the first digit cannot be 0 and the last digit cannot be 0.
Work out the number of different codes possible.
(Total for Question 22 is 3 marks)
Mark scheme · 6.3D The Product Rule for Counting: Fluency and Exam Drill

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20

Question 21

Question 22