PUSAT TUISYEN NEWTON
No. 17A, Jalan Indah 16/12, Taman Bukit Indah
Contact: 07 – 234 9168
FORM 5
Chapter 6: Permutation and Combination
6.2: Combination
The number of combination of r objects chosen from n different objects is given by:
n 𝑛!
Cr =
(𝑛−𝑟)!𝑟!
Example 7: Solve the followings.
8 7
1) C3 = 2) C4 =
Example 8: Differentiate and solve between permutation and combination cases
1) Calculate the number of ways to select 4 2) Calculate the number of ways to arrange 4
players from a group of 7 badminton players in a row from a group of 7
players for a double match. badminton players for a photography
session
3) Find the number of pairs of tennis double 4) Eugene wants to choose four souvenirs
players that can be formed from a group of from six different souvenirs. Calculate the
7 tennis players. number of different choices that she can
make.
Example 9: Solve the followings.
1) A committee that consists of 6 teachers is to be
chosen from 7 male teachers and 5 female teachers.
Find the number of different committee that can be
formed if
a) there is no restriction
b) 3 male teachers and 3 female teachers are required
in the committee
2) A Mathematics exam paper consists of 9 questions.
Find the number of combinations to answer 5
questions if a student
a) can answer any 5 questions
b) is required to answer 3 questions from Section A
which consists of 5 questions and 2 questions from
Section B which consists of 4 questions.
3) A group of suitable candidates consists of 5 men
and 6 ladies. A committee that consists of 2 men
and 3 ladies is to be formed from these suitable
candidates. Find the number of different
committees that can be formed.
4) Two lines are parallel. On the first line, there are 2
points, P and Q. On the second line, there are 6
points, A, B, C, D, E and F. Calculate the number
of triangles that can be formed by drawing straight
lines that pass through any 3 points.
5) Jack wants to choose 7 compact discs from 5 local
discs and 9 foreign compact discs. Calculate the
number of different choices is his choices must
have at least 3 local compact discs
6) Six members of a committee of a school are to be
selected from 6 male teachers, 4 female teachers
and a male principal. Find the numbers of different
committees that can be formed if
a) the principal is the chairman of the committee
b) there are exactly 2 females in the committee
c) there are not more than 4 males in the committee
7) A tour study group that consists of 8 people is to be
selected from 4 male teachers, 3 female teachers, 5
male students and 6 female students. Find the
number of different ways to form the group if it
consists of
a) 3 males
b) 2 teachers and 6 students
c) The same number of male teacher, female teachers,
male students and female students
8) A tennis team that consists of 8 students is to be
chosen from a group of 8 Form Four students and 6
Form Five students. Calculate the number of teams
that can be formed if
a) the team must consist of exactly 5 Form Four
students
b) the number of Form Four students in the team must
be more than the number of Form Five students.
9) A committee that consists of 6 members is to be
selected from 5 teachers and 4 students. Find the
number of different committees that can be formed
if
a) there is no restriction
b) the number of teachers must exceed the number of
students
10) A badminton team consists of 8 students is to be
chosen from a group of 7 male students and 6
female students. Calculate the number of different
teams that can be formed if each team must consist
of
a) exactly 3 male students
b) not more than 2 female students
11) A school chess team consists of 8 students is to be
chosen from a group of 7 male students and 6
female students. Calculate number of different
teams that can be formed if each team must consist
of
a) 4 male students
b) not less than 5 female students.
HOMEWORK (PERMUTATIONS AND COMBINATIONS)
1) A group of scouts consisting of 12 members is divided into three groups consisting of 5, 3 and
2 members in each group. In how many ways can the scouts be divided in these three groups?
2) Amin has 6 different storybooks and 5 different reference books. In how many ways can Amin
arrange 4 story books and 3 reference books in the order as shown below:
Storybook Reference Storybook Reference Storybook Reference Storybook
3) The PIBG of SMK Sri Kenanga committee consists of 8 members chosen from 6 teachers and 8
parents. In how many ways can the
a) committee be formed?
b) committee be formed if 2 science teacher and 2 maths teachers must be included
4) How many ways can all the letter in the word KEMBOJA be arranged in a row if the three
vowel are to be next to each other.
5) Mustafa wants to give his friends 6 stamps from his collection which consists of 4 stamps from
Philippines, 3 stamps from France and 5 stamps from Brunei. In how many ways can Mustafa
choose the 6 stamps if
a) 3 stamps from Brunei are to be chosen?
b) 2 stamps from each of the countries are to be chosen?
c) 2 stamps from the Philippines and one stamp from France are to be chosen
6) Sports equipment shop sells 4 brands of shuttlecocks, 3 brands of tennis balls and 5 brand of
ping-pong balls. In how many ways can the boxes containing the shuttlecocks, tennis balls and
ping-pong balls be displayed in the order as shown below:
shuttle ping pong shuttle tennis tennis ping pong
cocks balls cocks balls balls balls
7) 5 students are to be selected from 5 boys and 7 girls to receive free tickets to watch the
Airplane’s Exhibition in Langkawi.
a) In how many ways can the selection be made?
b) If the free tickets are to be given to two boys and three girls, calculate the number of ways
the selection can be made
8) A chess team consisting of 6 members is chosen from 7 boys and 4 girls. In how many ways
can the team be formed if
a) no condition is imposed?
b) the team needs to have at least 4 boys?
9) A committee consisting of 7 members is to be selected from 5 male teachers and 7 female
teachers. Calculate the number of different ways the committee can be formed if
a) the committee consists of 4 female teachers and 3 male teachers,
b) the committee consists of 5 female teachers and 2 male teachers and Puan Sharifah, Puan
Lim and Encik Rajan must be in the committee.
EXTRA PRACTICE
1) In how many ways can all the letters of the word ‘JUPITER” be arranged? How many of these
arrangement end with a vowel?
2) Six boys, of which 2 are twin brothers, are to be seated on 6 chairs arranged in a row. Find the
number of ways the boys can be arranged if
a) no conditions are imposed
b) the twin brothers must sit next to each other.
3) How many 4-digit numbers can be formed using the digits 4, 5, 6, 7, 8 and 9 if
a) repetition of digit is allowed
b) repetition of digit is not allowed.
4) How many 5-digit even numbers can be formed using the digits 4, 5, 6, 7, 8 and 9 if
a) repetition of digit is allowed
b) repetition of digit is not allowed.
5) Ali bought 10 red bulbs and 3 blue bulbs. He chooses 5 bulbs to be fixed in his room. In how
many ways can the bulbs be chosen if the number of red bulbs must be more than the number
of blue bulbs?
