Printable · GCSE Foundation · ages 14-16
Systematic listing and the product rule for counting worksheet — GCSE Foundation
Fifteen questions on "systematic listing and the product rule for counting" — DfE statement N5. Print it, or print three versions so neighbours cannot copy by letter; the key gives the letter for each version.
part HigherNon-calculator
Systematic listing and the product rule for counting worksheet — GCSE Foundation
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- 1.A bag holds 5 different sweets. Noah takes 2 of the sweets out of the bag together, so the order in which he takes them does not matter. Work out how many different pairs of sweets he could take.
- 2.By listing systematically, work out how many two-digit multiples of 5 can be made using the digits 0, 3 and 5, if each digit can be used at most once and the number cannot start with 0.
- 3.Two fair six-sided dice are rolled and their scores are added together. By listing the possible totals systematically, work out how many different totals are possible.
- 4.A café offers sandwiches with one filling from 5 choices and one type of bread from 4 choices. Cheese and mustard, which is one of the 5 fillings, is not available on gluten-free bread, which is one of the 4 breads. Work out how many different sandwiches are possible.
- 5.Two-digit numbers are made using the digits 1, 2, 3 and 4, and no digit may be used twice in the same number. Work out how many different two-digit numbers can be made.
- 6.A photography studio offers 4 backdrops and 3 outfits for a portrait session. The plain grey backdrop, one of the 4 backdrops, cannot be used with the formal suit outfit, one of the 3 outfits. Work out how many different backdrop-and-outfit combinations are possible.
- 7.A three-digit code is made using the digits 1, 2 and 3, and each digit may be used more than once. Work out how many different three-digit codes can be made.
- 8.Sara has a red T-shirt, a blue T-shirt and a green T-shirt. She has black shorts and grey shorts. By listing the combinations systematically, work out how many different outfits of one T-shirt and one pair of shorts she can make.
- 9.A vending machine sells 4 types of crisps, 5 types of chocolate bar and 2 types of drink. Work out how many different combinations of one crisp packet, one chocolate bar and one drink can be bought.
- 10.Two-digit numbers are formed using the digits 2, 5, 7 and 8, and each digit may be used only once in a number. Work out how many of these two-digit numbers are even.
- 11.Using only 20p coins and 10p coins, and at least one of each, work out how many different ways there are to make exactly 60p. List the possibilities systematically.
- 12.A spinner has 4 colours and a coin has 2 sides. Work out how many different outcomes are possible when the spinner is spun once and the coin is tossed once.
- 13.A café offers 3 types of soup and 4 types of bread roll. Work out how many different combinations of one soup and one bread roll are possible.
- 14.A car manufacturer offers a car in 6 colours and 4 trim levels. Two colour-and-trim combinations are not available: red with sport trim, and white with sport trim. Work out how many different colour-and-trim combinations are available.
- 15.A café sells ice cream in three flavours: vanilla, mango and pistachio. Isla buys a cone with two scoops, using two different flavours, one for the bottom scoop and one for the top scoop. Work out how many different cones she could buy.
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