Counting

Exercise 1

A test consists of $6$ multiple choice questions. Each question has four possible answers; only one of them is correct.

a

Use a road diagram to chart all possibilities.

b

How many possible answer series are there?

c

You have prepared well for the test and you are certain about $4$ answers. How many possible answer series remain?

d

Noting only 'correct' or 'wrong', how many answer series are possible?

Exercise 2

To open the combination lock of a suitcase you need to remember a four digit code.

a

You only remember the first digit. How many possible codes remain?

b

You know all four digits, but don't remember the order they are in. How many possible codes are there?

Exercise 3

You throw three regular dice.

a

Draw up a road diagram of all possible outcomes.

b

Why is a tree diagram not useful in this case?

c

How many outcomes contain exactly one 6?

d

How many outcomes contain two sixes?

e

How many outcomes contain three sixes?

f

How many outcomes contain at least two sixes?

g

How many outcomes contain no more than two sixes?

Exercise 4

You order a pizza at Mario's. You can choose a small pizza, a regular pizza and an extra large pizza. There are two types of pizza crust: the "pizza crossa" and the "pizza classico". There are $12$ different flavours.
You can have the pizza delivered or pick it up yourself.

a

How many pizzas can you choose from at Mario's?

b

How many options do you have in total if you want to eat a pizza from Mario's?

c

You don't like fish. That reduces your choice of flavours by 5. How many pizza's can you now choose from?

Exercise 5

A slot machine has three windows behind which strips containing pictures spin around. Each strip has $20$ pictures. To let the strips rotate, you pull a handle. One push on a button stops the spinning of the strips. If the three pictures you see are equal you win a certain amount of money. The number of each of the pictures on each strip is noted as follows:

a

What is the total number of possible outcomes?

b

In how many ways can you get three BARs?

c

In how many ways can you get three oranges?

d

In how many ways can you get three times a cherry ?

e

How many outcomes give you a prize?

Exercises