This is a detailed lesson plan on Combination using Deductive Method.

1. LESSON PLAN FOR MATHEMATICS 10
I. INFORMATION
Subject Matter: Combination
Grade Level: X Time Allotment: 1 hour
Teacher/s: Elton John B. Embodo
Content Standard: The learner demonstrates understanding of key concepts of combinatorics and probability.
Performance Standard: The learner is able to use precise counting technique and probability in formulating
conclusions and making decision.
Learning Competency: The learner illustrates the combination of objects. (M10SP-IIIe-1)
Objectives: At the end of the lesson, the students must have:
a. illustrated the combination of objects; and
b. explained the relevance of combining objects in real life.
References: A (2021, October 4). Combination in Math- Definition, Formula and Example. BYJUS.
https://byjus.com/maths/combination
Instructional Materials: PowerPoint, chalk
Skills: Analysis and Collaboration
Values: Unity, cooperation, camaraderie
Method: 3Is Method
II. LEARNING EXPERIENCES
Teacher’s Activity Students’ Response
A. Introduction
1. Prayer
2. Greetings
3. Reminders
4. Checking of Attendance
5. Classroom Rules - MATH
Must come to class neat, clean, and prepared.
Actively participate in the activities and pay attention to the
discussion.
Talk appropriately and respectfully to your teacher and
classmates.
Handle the learning materials with care.
Are my rules clear to you class?
a. Review
In our previous meeting, we discussed the process of
illustrating the permutation of objects.
Can anybody here recall what permutation is?
Absolutely!
Who would like to illustrate the formula of the permutation?
To assess whether you can still recall on how to illustrate the
permutation of objects, I have here an example. And I want
somebody to solve it on the board.
Yes sir!
Permutation is an arrangement of objects in a definite
order.
!
Pr
( )!
n
n
n r



2. That is awesome! Therefore, there are 60 3-letter words can
be formed from the word SWING without repetition of the
letters.
b. Motivation
This time class, I need 5 volunteers to stand here in front. I
will consider them as five members of a certain group.
Now, I am going to rearrange their positions.
The first student from the left will exchange position with
fifth one, and the second one will exchange position with the
fourth one.
With their new arrangement class, do I still get the same
members of the group?
That is right, I still get the same members of the group even
if I swapped their positions.
(The volunteers are told to go back to their chairs)
In other specific cases class, do you know on how to select
objects or persons from a sample without regard to the
arrangement using a standard formula?
Do you know how to illustrate the combination of objects?
B. Interaction
So be with me this morning class as I discuss to you the
process of illustrating the combination of objects. Everybody
read!
Statement of the Aim
Listen attentively since you are expected to achieve the
following objectives. Everybody read!
Solution
!
Pr
( )!
n
n
n r


5!
Pr
(5 3)!
5 4 3 2!
Pr
(2)!
Pr 60
n
n
n


  


(The five students who volunteered are standing in front
of the class)
(The five students are being rearranged in terms of their
positions)
Yes sir, because they are not being replaced by other
students but they are just being rearranged.
No sir!
No sir!
“Combination”
How many 3 letter words with or without
meaning can be formed out of the letters of
the word SWING when repetition of letters
is not allowed?
Objectives:
a. illustrate the combination of objects; and
b. explain the relevance of combining
objects in real life.

3. Let us have first the definition of combination. Can somebody
read?
In simple words class, combination is the process of selecting
objects in which the order of selection is not important.
For us to be guided in illustrating the combination of objects,
I have here its formula.
!
r
( )! !
n
nC
n r r


Where;
C stands for combination of objects
n – refers to the size of the given sample from which the
selection of objects is to be taken
r – refers to the number of objects to be selected from the
given sample.
Giving of Examples
How many flavors are available for the milkshake? What are
these flavors?
Very good! So, the value of the n in the formula is 4 because
there are 4 available flavors for the milkshake. (n = 4)
Among these 4 available flavors, how many flavors are only
allowed to be combined in a single milkshake?
That is right, so we shall only have 3 flavors to combine for
a single milkshake. In other words, we only select 3 flavors
among the 4 available flavors. So, what is then the value of
the r in the formula?
(r = 3)
Absolutely! But now, the question is, how many possible
combinations of 3 flavors among the 4 available flavors for
the milkshake?
To answer the question, let us make use of the given formula.
So what do we have to do with the values of n and r?
Combination – is an arrangement of objects where the
order in which the objects are selected does not matter.
The combination means “Selection of things”, where the
order of things has no importance.
There are four available flavors for the milkshake which
are Apple, Banana, Cherry, and Durian.
According to the situation sir, the person is only allowed
to combine 3 flavors for a single milkshake.
Since we will only select 3 flavors among the 4
available flavors, the value of the r in the formula is 3.
1. Supposed you want to buy a milkshake and you
are allowed to combine any 3 flavors from Apple,
Banana, Cherry, and Durian. How many possible
combinations of three flavors from the available
flavors which are Apple, Banana, Cherry, and
Durian?

4. !
r
( )! !
n
nC
n r r


So this time, we will replace the n and r with 4 and 3
respectively.
4!
4 3
(4 3)!3!
C 

Let us simplify, what is (4-3)!?
Very good, so we now have
4!
4 3
1!3!
C 
So, what shall we do with 4! so that it will be divisible by 3!?
Alright! So, we now have
4 3!
4 3
1!3!
C


So, what is 1!?
Fantastic! This time we have
4 3!
4 3
3!
C


This time, what shall happen to the 3! in the numerator and
the 3! in the denominator?
When similar or like terms are divided out, what is then the
quotient?
Perfect! So, the answer is 4 3 4
C  .
What does it mean then?
Since there are 4 possible combinations of 3 flavors, can
anybody illustrate here the exact 4 combinations of 3 flavors
for the milkshake?
This time, I want somebody to solve it on the board while the
rest should also solve on their seats.
We will substitute them to the formula sir.
(4-3)! is equal to 1!
We will simplify the 4! into 4∙3!.
1! sir is equal to 1.
They will be divided out sir since they are like terms.
The quotient sir is 1.
It means sir that there are 4 possible combinations of 3
flavors for the milkshake from 4 available flavors.
1. Apple, Banana, & Cherry,
2. Apple, Banana, & Durian,
3. Apple, Cherry, & Durian
4. Banana, Cherry, and Durian
2. In a 10-item mathematics problem-solving test
how many ways can you select 5 problems to
solve?

5. Fabulous! Let give your classmate a “3 claps”.
Collaborative Activities
Here are the mechanics for the group the activity. Everybody
read!
Presentation of Group Outputs
The sequence will depend on which group finishes first.
(The teacher verifies the students’ outputs after the
presentation)
!
r
( )! !
10!
10 5
(10 5)!5!
10 9 8 7 6 5!
10 5
5!5!
30240 5!
10 5
120 5!
30240
10 5
120
10 5 252
n
nC
n r r
C
C
C
C
C




    






(Students present their group outputs)
1. The class will be divided into three
groups.
2. Each group will be given with
different problems to be solved in
3 minutes.
3. The group which can finish solving
the problem first with correct
solutions and answers will be
declared as the winner.
4. Each group must select one
representative to explain the output
in front.
Group 1
A group of 3 lawn tennis players S, T, U.
A team consisting of 2 players is to be
formed. In how many ways can we do so?
Group 2
Find the number of subsets of the set {1, 2,
3, 4, 5, 6, 7, 8, 9, 10} having 3 elements.
Group 3
In how many ways can a coach choose
three swimmers from among five
swimmers?

6. Prepared:
ELTON JOHN B. EMBODO
C. Integration
Values Integration
A while ago class, we discussed the combination of objects
in which we select objects from a sample without regard to
the order.
Now class, can you share some of your experiences when you
combine objects to form a new set of groups for a very
important purpose?
In the combination class, we select objects without regard to
their order, can you share other experiences when you select
objects without minding their order?
All your ideas class are amazing. Yes, sometimes in life, we
do not regard to the order of things or objects as we select or
treat them.
Just like for the parents in treating their children. Regardless
of who the youngest or the oldest is, their love for their
children is equal.
Do have any clarification class?
(Students have different answers)
(Students have different answers)
No sir!
III. EVALUATION
Directions: In a one whole sheet of paper, illustrate the combination of objects indicated in the following items.
1. Picking 6 balls from a basket of 12 balls.
2. Forming a committee of 5 members from 20 people.
3. Choosing three of your 14 classmates to attend your party.
4. How many different sets of 5 cards each can be formed from a standard deck of 52
cards?
5. In a 10-item mathematics problem-solving test, how many ways can you select 5
problems to solve.
Answers:
1. 924
2. 15504
3. 364
4. 2598960
IV. ASSIGNMENT
Directions: In a one-half sheet of paper, differentiate the permutation and combination using a Venn Diagram. Submit
your answer next time.