# Exam-Style Questions on Combinations

## Problems on Combinations adapted from questions set in previous Mathematics exams.

### 1.

GCSE Higher

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?

### 2.

GCSE Higher

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.

### 3.

GCSE Higher

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.

The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.

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