2.3 Systematic listing strategies — Practise

Work independently, then use the checked solutions to review your method.

1. A badge has one of two shapes, circle or star, and one of three colours, red, blue or green. List all possible badges.
2. List all three-digit numbers made from $2,4,6$, using each digit once.
3. A snack can be a yoghurt or a biscuit, with water, juice or milk. List every snack-and-drink choice.
4. A journey has a choice of two trains, A or B, and one of two buses, X or Y. List the possible train-and-bus pairs.
5. List all two-digit numbers made from $1,2,3,4$ without repeating a digit.
6. There are three paths from A to B and two paths from B to C. List the route choices from A to C using labels A1, A2, A3 and B1, B2.
7. Three runners, Ana (A), Ben (B) and Cal (C), finish first, second and third with no ties. List all possible finishing orders.
8. Using digits $1,2,3$ once each, list the three-digit numbers that are even.
9. A menu has two starters (soup, salad), two mains (rice, pasta) and two desserts (fruit, cake). List the meals with salad and fruit.