Exam-Style Questions on Combinations

Students in Year 10 at Riverdale High School can choose two different courses for their Friday afternoon elective lessons. Their two choices must be from two different school departments.

• The Physical Education department offers 5 different courses;
• The Performing Arts department offers 6 different courses;
• The Science department offers 4 different courses.

How many different ways are there of choosing two courses?

Worked Solution

A restaurant offers 6 starters, 14 main courses and 5 different desserts.

The promotion of the month offers a discount on certain meals. A customer can choose from one of the following:

• a starter and a main,
• a main and a dessert,
• a starter and a dessert.

Show that there are 184 different ways of choosing a meal for this promotion.

Worked Solution

Michael decides to order a starter and a main course from the restaurant menu.

On the menu there is a choice of 12 different starters.

Michael thinks that there are enough main courses to provide exactly 222 different ways of choosing one starter and one main course.

Could Michael be correct?

You must show all of the working you would use to show how you arrived at your answer.

Worked Solution

Patty O'Dores is reading the menu in a restaurant.

There are 4 starters, 9 main courses and some desserts on the menu.

Patty is going to choose one starter, one main course and one dessert.

She says there are 360 ways that she can choose her starter, main course and dessert.

How many desserts are on the menu?

Worked Solution

There are four dials on a combination lock.

Each dial can be set to one of the numbers 1, 2, 3, 4.

The four digit number 4234 is one way the dials can be set, as shown in the diagram.

(a) Work out the number of different four digit numbers that can be set for the combination lock.

(b) How many of the possible four digit numbers have four different digits?

Worked Solution