Combination and Permutation In grade 10 3rd quarter mathematics topic

1. WHAT IS PERMUTATION?
A Permutation is an arrangement of
items in a particular order.
Notice, ORDER MATTERS!
1
❑𝑛 𝑃𝑟 =
𝑛 !
(𝑛 −𝑟 )!

2. 2
OBSERVE THE TWO PROBLEMS.
1.In how many ways can 3 students be
chosen from 10 members of the group?
2.In how many ways can tops 1, 2, and 3 be
chosen from the 10 members of the group?
Which of the two problems involves arrangements?
Which among the problem is a permutation, and why?
How about the other one? Is it also a permutation? If not, what is it?
The other one is called a combination. How would you define a
combination?

3. COMBINATIONS
A combination is an arrangement
of an objects with no repetitions
and the order is NOT important.
3
❑𝑛 𝐶𝑟 =
𝑛 !
(𝑛− 𝑟 ) ! 𝑟 !

4. STATE WHETHER EACH OF THE FOLLOWING IS A
COMBINATION OR A PERMUTATION
Permutation
4
1.Arrangement of 10 people in a row.
2.A committee of 5 persons will be chosen from a group
of 7 persons.
3.A group of 45 people are going to run a race. The top
three runners earn gold, silver and bronze metals.
4.A team of 8 basketball players needs to choose a
captain and co-captain.
5.A hand of 13 cards having exactly 10 spades drawn
from a deck of cards.
Combination
Permutation
Permutation
Combination

5. STATE WHETHER EACH OF THE FOLLOWING IS A
COMBINATION OR A PERMUTATION
Combination
6. There are 45 applicants for three Computer
Programmer positions.
7. There are 110 people at a meeting. They each shake
hands with everyone else.
8. Arrangement of 8 people at round table.
9. Number of 4 different digits that can be formed from 6
different digits.
10. Number of circles determined by 10 points, no three
of which are collinear.
Combination
Permutation
Permutation
Combination

6. EVALUATE THE FOLLOWING.
6
❑𝑛 𝐶𝑟 =
𝑛!
(𝑛− 𝑟 ) !𝑟 !
=3 ways
=15ways
=84ways
=70 ways
=5 ways

7. EVALUATE THE FOLLOWING.
1. In how many ways can a principal choose 3 of
their 30 teachers to attend a conference abroad?
2. Six officers of the Mathematics Club are in a
conference room. If each one shakes hands with
each of the others once, how many handshakes
are possible?
3. How many committee of 4 persons can be chosen
from a group of 10 persons?
4. In how many ways can a committee of 5 person be
chosen from 7 single ladies and 9 men?
7
❑𝑛 𝐶𝑟 =
𝑛!
(𝑛− 𝑟 ) !𝑟 !
4,060 ways
15 ways
210 ways
4,368 ways

8. 8

9. 9