BICOL REGION (V) VALIDATED DLP

BOLO NORTE
School Grade Level: 10
NATIONAL HIGH SCHOOL
Writer: ROMEL P. PEÑA Learning Area: Mathematics 10
Teaching
February 21, 2025 4th Quarter
Dates and Quarter:
1:30- 2:30 Week 2 Day 5
Time:
I. Objectives

A. Content The learners demonstrate understanding of key

Standards concepts of combinatorics and probability.
B. Performance The learners are able to use precise counting technique and
Standards probability in formulating conclusions and making the
decisions.

C. Learning Illustrates the combination of the objects.

Competencies/
Objectives (Write M110SP-IIIb-1
the LC code for Learning objectives:
each)
At the end of the lesson 75% of the students will be able to;

• Define combination of the object.

• Solving using the formula of combination; and
• Apply the concept of combination in real life problem.

II. Content (Subject Combinations of an Object

Matter)
III. Learning
Resources
A. References

1. Teacher’s Teachers Guide in Mathematics 10 page 310

Guide Page
2. Learners’ Learners Materials in Mathematics 10 page 310
Material Page
3. Additional
Materials from
Learning
Resource
(LR) Portal
B. Other Learning Cartolina, Television, laptop and cellphone
Resources
C. Values Integration

D. Subject Values Education, MAPEH, English,

Integration
IV. Teacher’s Activities Student’s Activities

A. Preliminary Greetings
Activities Good afternoon, sir!
Good afternoon, class!
 Prayer
Before we begin our
discussion, everyone please
In the name of the father…
stand and let’s pray first.
Amen.
Mark pls lead the prayer

Classroom management
Before you take your seats,
please arrange your chairs
properly and pick the pieces Thank you, sir!
of paper and dirt under your
chair.
You may now take your seat. We are good, Sir!

Checking of attendance
How are you today class? None, sir!

Are there any absences

today?
Okay, very good everyone.

B. Motivation
C. Development of Presentation of the Lesson
the Lesson
Combinations of an Object Students are listening

EXPLORE EXPLORE
DIRECTION: Read and
analyze each item carefully.
Write the letter of the correct
answer on the blank
provided before each
number.
1. Which of the following
determines the number of
possible groups of a
collection of items where the
order of the elements does
not matter?
A. FCP
B. Permutation
C. Combination
D. Probability
2. Which of the following
requires combination?
A. Entering the PIN of your
ATM card.
B. Arranging three people to
pose for a picture.
C. Choosing 3 of your
friends to attend to your
birthday party.
D. Forming 3-digit numbers
from the digits 1, 2, 3, 4, 5,
6, ad 7.
3. Selecting two
representatives from 8
candidates requires ______.
A. FCP
B. Permutation
C. Combination
D. Probability
4. The number of
combinations of n objects
taken r at a time is defined
by the expression _____.
𝑛!
a.
𝑟!

𝑛!
b. (𝑛−𝑟)!𝑟!

𝑛!
c. (𝑛−𝑟)!

d. n!
We obviously know what
How did you find the combination is.
activity?
Very Good, Class

EXPLAIN EXPLAIN
Let’s define first what is The class reads the
Combination. definition of combination.
Combination is a selection
made from a group of items
without regard to their order.
Combination is denoted by Students are listening.
nCr and read as s “the
combination of n objects
taken r at a time” or “n
choose r”.
Examples that describes
combination.
1. Selecting of players in any
order. Students are observing.
2. Playing Lotto.
3. Creating Committees
Who can give me another
example representing
combination?
These are the examples that Answers may vary.
describes combination.
How can we solve the
Students are listening.
combination?
Formula of combination.
𝑛!
nCr =
(𝑛−1)!𝑟!

where:
C refers to the number of
combinations.
n refers to the total number
of objects in a set. None, Sir!
r refers to the number of
objects selected from the set
Any questions, class?

ELABORATE ELABORATE
Solving problems
involving combination.
Example 1.
Three Players were
numbered as 1, 2, and 3,
how many teams of two
players can be formed?
The arrangement of team
members can affect the No, Sir?
team composition? Yes or
No?
Because we are going to
Why? arrange the members only.
Then we are going to find
how many teams can be
formed consisting of two
players

Solution:
n= 3, r= 2
Formula:
𝑛!
nCr =
(𝑛−𝑟)!𝑟!

3! 3×2! 3×2!
nCr = (3−2)!2! (1)!2! = =3
2!

There are 3 teams can be

formed
Let’s illustrate how the
combination of that example
arrives at 3 combinations.
Note: Players 1 and 2
forming a team is the same
as the team formed by
players 2 and 1. Thus, order
is NOT important. Listing
possible arrangements, they
are:

Yes, Sir.
Did you understand the
concept of combination?
Example 2.
Lotto is a game of chance
which is played by choosing
six different numbers from 1
to 42. How many different
bets are possible? Use
Scientific Calculator in
solving this example.
Who got the correct answer
Each group are solving
first will be having 1 strip
every member of each The group that got the
group. correct answer is explaining
in front.
Solve it by group then,
explain. Solution:
n= 42, r= 6
Formula:
𝑛!
nCr =
(𝑛−𝑟)!𝑟!

42! 42!
42C6 = =
(42−6)!6! 36!6!
=
𝟓, 𝟐𝟒𝟓, 𝟕𝟖𝟔
Example 3
How many combinations of
Each group are solving with
three letters can be made
their teammate.
from the letters B, E, A, U, T,
and Y? The group got the correct
answer is explaining in front.
Then explain how you
arrived on your answer. Solution: n= 6 , r= 3
Formula:
𝑛!
nCr =
(𝑛−𝑟)!𝑟!

6! 6! 6!
42C6 = =
(6−3)!3! 3!3!
= =
3!3!
6!
= 𝟐𝟎
36

Thank you so much!

Yes, Sir!
Did you understand our
lesson for today?
Do you have any Question? None, Sir!

Generalization:
Since there are no questions The answers may vary.
regarding for our lesson.
Who can give me, what you
have learned today?

EVALUATE EVALUATE
Answer the following Expected answer.
questions. Show your
solution if needed.
 1. Which of the following 1. C
situation does not require
2. D
combination?
3. 220
A. Forming a committee of
councilors. 𝑛!
4. nCr = (𝑛−1)!𝑟!
B. Assigning rooms to
conference participants. 5. 21

C. Selecting the top 3

winners in a singing contest.
D. Choosing two literature
books to buy from a variety
of choices.
2. Which of the following
requires combination?
A. Issuing plate numbers.
B. Lining up in paying bills.
C. Arranging 6 people in a
round table.
D. Choosing five badminton
players from 12 athletes.
3. Evaluate: 12𝐶3.

4. The number of
combinations of n objects
taken r at a time is denoted
by ________.
5. How many straight lines
can be drawn using the 7
points X, Y, Z, M, N, O, and
P, such that no three points
are collinear?

VI. Assignment Answer the following.

1. How many different
committees of 4 people
can be formed from a pool
of 7 people?
2. How many different
committees consisting of 8
people can be formed
from 12 men and 9
women if the number of
men and the number of
 women as members are
equal?
3. A committee of 3
members is to be formed
from 6 women and 5 men.
The committee must
include at least 2 women.
In how many ways can
this be done?

VII. Remarks

VIII. Reflections

A. No. of learners
who earned 80%
in the evaluation
B. No. of learners
who require
additional
activities for
remediation who
scored below
80%
C. Did the remedial
lessons work?
D. No. of learners
who continue to
require
remediation
E. Which of my
teaching
strategies worked
well? Why did
these work?
F. What difficulties
did I encounter
which my
principal or
supervisor can
help me solve?
G. What innovation
or localized
materials did I
use/discover
which I wish to
share with other
teachers?
Prepared by:
Jerick B. Magadia
Mathematics Student Teacher

Reviewed by:
Janet N. Buatis
Resource Teacher