Problems adapted from questions set for previous Mathematics exams.
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.
How many different ways are there of choosing two courses?
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:
Show that there are 184 different ways of choosing a meal for this promotion.
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.
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?