Revision NotesExam QuestionsPast Papers
IGCSEAdditional MathsCIEExam QuestionsSequences & SeriesPermutations & Combinations

Permutations & Combinations (CIE IGCSE Additional Maths)

Exam Questions

1 hour16 questions
Medium
Hard
Very Hard
1
Sme Calculator2 marks

In an examination, candidates must select 2 questions from the 5 questions in section A and select 4 questions from the 8 questions in section B. Find the number of ways in which this can be done.

How did you do?

Did this page help you?

2
Sme Calculator2 marks

The digits of the number 6 378 129 are to be arranged so that the resulting 7-digit number is even.
Find the number of ways in which this can be done.

How did you do?

Did this page help you?

3
Sme Calculator4 marks
(i)
Find how many different 5-digit numbers can be formed using five of the eight digits 1, 2, 3, 4, 5, 6, 7, 8 if each digit can be used once only.

[2]

(ii)
Find how many of these 5-digit numbers are greater than 60 000.

[2]

How did you do?

Did this page help you?

1
Sme Calculator2 marks

A team of 3 people is to be selected from 4 men and 5 women. Find the number of different teams that could be selected which include at least 2 women.

How did you do?

Did this page help you?

2
Sme Calculator4 marks

A committee of 5 people is to be formed from 6 doctors, 4 dentists and 3 nurses. Find the number of different committees that could be formed if

(i)
there are no restrictions,

[1]

(ii)
the committee contains at least one doctor,

[2]

(iii)
the committee contains all the nurses.

[1]

How did you do?

Did this page help you?

3
Sme Calculator3 marks

Find the number of ways in which 12 people can be put into 3 groups containing 3, 4 and 5 people respectively.

How did you do?

Did this page help you?

4a
Sme Calculator1 mark

A 4-digit code is to be formed using 4 different numbers selected from 1, 2, 3, 4, 5, 6, 7, 8 and 9. Find how many different codes can be formed if 

there are no restrictions,

How did you do?

4b
Sme Calculator1 mark

only prime numbers are used,

How did you do?

4c
Sme Calculator2 marks

two even numbers are followed by two odd numbers,

How did you do?

4d
Sme Calculator2 marks

the code forms an even number,

How did you do?

Did this page help you?

5
Sme Calculator5 marks
(i)
Find how many different 5-digit numbers can be formed using the digits 1, 3, 5, 6, 8 and 9. No digit may be used more than once in any 5-digit number.

(ii)
How many of these 5-digit numbers are odd?

(iii)
How many of these 5-digit numbers are odd and greater than 60 000?

How did you do?

Did this page help you?

6
Sme Calculator6 marks
(i)
Find how many different 4-digit numbers can be formed using the digits 2, 3, 5, 7, 8 and 9, if each digit may be used only once in any number.

[1]

(ii)
How many of the numbers found in part (i) are divisible by 5?
[1]

(iii)
How many of the numbers found in part (i) are odd and greater than 7000?
[4]

How did you do?

Did this page help you?

7
Sme Calculator6 marks
(i)
Find how many different 5-digit numbers can be formed using the digits 1, 2, 3, 5, 7 and 8, if each digit may be used only once in any number.

[1]

(ii)
How many of the numbers found in part (i) are not divisible by 5?

[1]

(iii)
How many of the numbers found in part (i) are even and greater than 30 000?

[4]

How did you do?

Did this page help you?

8
Sme Calculator4 marks
(i)
Find how many different 4-digit numbers can be formed using the digits 1, 3, 4, 6, 7 and 9.
Each digit may be used once only in any 4-digit number.

[1]

(ii)
How many of these 4-digit numbers are even and greater than 6000?

[3]

How did you do?

Did this page help you?

9
Sme Calculator5 marks

4-digit numbers are to be formed using four of the digits 2, 3, 7, 8 and 9. Each digit may be used once only in any 4-digit number. Find how many 4-digit numbers can be formed if

(i)
there are no restrictions,

[1]

(ii)
the number is even,

[1]

(iii)
the number is greater than 7000 and odd.

[3]

How did you do?

Did this page help you?

1a
Sme Calculator4 marks

A photographer takes 12 different photographs. There are 3 photographs of sunsets, 4 of oceans and 5 of mountains.

The photographs are arranged in a line on a wall.

(i)
Find the number of possible arrangements if the first photograph is of a sunset and the last photograph is of an ocean.

(ii)
Find the number of possible arrangements if all the photographs of mountains are next to each other.

How did you do?

1b
Sme Calculator4 marks

Three of the photographs are selected for a competition.

(i)
Find the number of different possible selections if no photograph of a sunset is chosen.

(ii)
Find the number of different possible selections if one photograph of each type (sunset, ocean, mountain) is chosen.

How did you do?

Did this page help you?

2
Sme Calculator4 marks

Given that 45 space cross times space straight C presuperscript n subscript 4 equals space open parentheses n plus 1 close parentheses space cross times to the power of n plus 1 end exponent straight C subscript 5, find the value of n.

How did you do?

Did this page help you?

3
Sme Calculator4 marks

The number of combinations of n items taken 3 at a time is 92 n. Find the value of the constant n.

How did you do?

Did this page help you?

4
Sme Calculator4 marks

The number of combinations of n items taken 3 at a time is 6 times the number of combinations of n items taken 2 at a time. Find the value of the constant n.

How did you do?

Did this page help you?