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Permutations & Combinations (Cambridge O Level Additional Maths)

Exam Questions

1 hour16 questions
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1
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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.

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2
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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.

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3
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(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]

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1
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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.

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2
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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]

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

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4a
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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,

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4b
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only prime numbers are used,

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4c
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two even numbers are followed by two odd numbers,

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4d
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the code forms an even number,

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5
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(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?

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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]

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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]

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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]

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9
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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]

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1a
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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.

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1b
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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.

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2
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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.

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

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4
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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.

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