Cambridge IGCSE · Mathematics - Additional (0606)

Permutations and combinations: Practice Questions

5 multiple-choice questions marked as you go, and 5 written questions with worked solutions. All on Permutations and combinations.

10 questions26 marksFree, no account

Question 1

1 mark

Calculate the number of different ways all the letters of the word VECTOR can be arranged in a line.

Question 2

1 mark

How many different 4-digit numbers can be formed using the digits 1, 3, 5, 7, 8, and 9, if each digit can be used only once and the number must be even?

Question 3

1 mark

A committee of 5 members is to be chosen from a group of 6 men and 4 women. Find the number of different ways the committee can be formed if it must contain at least 3 women.

Question 4

1 mark

Find the number of different 5-letter arrangements that can be formed using all the letters of the word ORBIT if the first letter must be a vowel.

Question 5

1 mark

Four men and three women are to stand in a straight line for a photograph. Calculate the number of different ways they can be arranged if no two women are to stand next to each other.

Question 6

2 marks

A student has 7 different posters to display. Find the number of ways that 3 of these posters can be selected and arranged in a row on a wall.

Write your answer out first, then check it against the worked solution.

Question 7

4 marks

A password is to be formed using 4 characters from the set \(\{A, B, C, D, E, 1, 2, 3\}\). No character can be repeated. Find the number of different passwords that can be formed if the password must start with a letter and end with a digit.

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Question 8

6 marks

Consider the letters of the word CHAMPION. Find the number of different 8-letter arrangements that can be made if the vowels (A, I, O) must not be next to each other.

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Question 9

4 marks

A sports club needs to select its leadership for the upcoming season from a group of 12 eligible members.
(a) Find the number of ways to choose a chairperson and a secretary.
(b) Find the number of ways to choose a committee of 3 members from the remaining 10 members.

Write your answer out first, then check it against the worked solution.

Question 10

5 marks

There are 12 points marked in a plane. 5 of these points lie on a single straight line \(L\), and the other 7 points are scattered such that no three points (including those on \(L\)) are collinear. Find:
(a) The number of different straight lines that can be formed by joining any two points.
(b) The number of different triangles that can be formed using these points as vertices.

Write your answer out first, then check it against the worked solution.

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