Permutations & Combinations (Cambridge (CIE) O Level Additional Maths): Exam Questions

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.

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]

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

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,

only prime numbers are used,

two even numbers are followed by two odd numbers,

the code forms an even number,

(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?

(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]

(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]

(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]

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]

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.

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.

Given that , find the value of .

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

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