DAILY SCHOOL BAUTISTA NATIONAL HIGH Grade Level & 10- BALTAZAR

LESSON SCHOOL Section

PLAN STUDENT JEROMEF. JIMENEZ Learning Area MATHEMATICS
TEACHER

Time allotment THURSDAY (January 5, Quarter 3

2022) 9:50 -10:50 AM
I. OBJECTIVES
A. Content The learners demonstrate an understanding of key concepts of
Standards combinations: forming conclusions and making decisions.
B. Performance The learners shall be able to solve problems involving
Standards combinations.
C. Learning differentiate permutation from combination; and
Competencies illustrate the combination of n objects.
D. Objectives At the end of the lesson, the students should be able to:
a. derive the formula for finding the number of
combinations of n objects taken r at a time.
II. CONTENT COMBINATIONS
III. LEARNING
RESOURCES
A. References
1. Teachers Guide pp. 301-309
pages
2. Learner’s pp. 301-309
Material pages
B. Other Learning Grade 10 Mathematics Learner’s Module
Resources
IV. PROCEDURES Teacher’s Activity Learner’s Activity
A. Reviewing the ELICIT The teacher will have a The learners will
previous lesson or short recap about the recall and recite to
presenting the new topic last discussed solve problems
lesson which is about involving
Permutation. permutations.

B. Establishing a ENGAGE Motivation: The teacher Group Spelling

purpose for the will let the learners play
lesson the Group Spelling. The
class will be divided into
two groups.
C. Presenting
examples/instances Group spelling. I will ask
of the new lesson each group to spell the Spell the word
word combinations, this “COMBINATIONS”
spelling will be in chorus
that one member must
only mention one letter
from the word
combinations, strictly
without giving signs to
one another, the fastest
group that will spell the
word will win.

After the game, the

teacher will introduce to
the class the lesson and
explain the concepts of
Combinations.
D. Discussing new EXPLORE Activity 1: Identify
concepts and AND whether the following
practicing new EXPLAIN sentences involve
skills #1 permutation or
combination. Answers:

E. Discussing new 1. Opening a 1. Permutation

concepts and combination lock.
practicing new 2. Winning in a contest 2. Permutation
skills #2 3. Assigning seats to
guests at dinner. 3. Combination
4. Listing the elements
of subsets of a 4. Combination
given set.
5. Selecting 3 posters
to hang out of 6 5. Combination
different posters.

A. COMBINATORIC
S
Combinatorics
is the branch of
mathematics studying
the enumeration,
combination, and
permutation of sets of
elements and the
mathematical relations
that characterize their
properties.
Mathematicians
sometimes use the term
"combinatorics" to refer
to a larger subset of
discrete mathematics
that includes graph
theory.

A combination is a
mathematical technique
that determines the
number of possible
arrangements in a
collection of items where
the order of the selection
does not matter. In
combinations, you can
select the items in any
order. Combinations can
be confused with
permutations.

Scenario:
Suppose you were
 assigned as the leader
and have the freedom to
choose 4 of your
classmates to be your
group mates. If you
choose Aira, Ferie,
Lorrea, and Daniel, does
it make any difference if
you choose Ferie,
Lorrea, Daniel, and Aira?
Of course not, because
the list refers to the
same people. Each
selection that you could
possible make is called
combination. On the
other hand, if you
choose Aira, Johana,
Shaina, and Jenilyn,
now that is another
combination, and it is
different from the first
combination cited.

Remember: If there is a
set S with n elements,
and if r is a nonnegative
integer less than or
equal to n, then each
subset of S containing r
distinct elements is
called a combination of
S.

The number of
combinations of n
objects taken r at a time
is denoted by
C(n,r)

Suppose now, form a

triangle given 4 points
plotted, say, A, B, C, and
D, of which no three are
collinear.
We can say that ABC,
is the same as BCA and
CBA. In the same
manner, BCD is the
same as CBD and DBC.
This is another
illustration of
combination. The
different triangles that
can be formed are ABC,
 ABD, BCD, and CDA.
Thus, there are 4
combinations.

Note:
There are 4 objects (A, B,
C, D). n=4
They are selected 3 at a
time. r=3
And so the equation
becomes C(4,3).

Formula:
P (n , r)
C(n,r) =
r!

n!
C(n,r) = ( n−r ) !
r!

n!
C(n,r) =
r ! ( n−r ) !

Example 1:
In how many ways
can a committee
consisting of 4 members
be formed from 8
people?

P (8 , 4)
C(8,4) =
4!

8!
C(8,4) = ( 8−4 ) !
4!

8!
C(8,4) =
4 ! ( 8−4 ) !

C(8,4) =
8 ∙7 ∙ 6 ∙5 ∙ 4 ∙ 3 ∙2 ∙ 1
4 ∙ 3 ∙2 ∙1 4 ∙3 ∙ 2∙ 1

7 ∙5 ∙ 2
C(8,4) =
1

C(8,4) = 70 ways

Example 2:
How many polygons
 can be possibly formed
from 6 distinct points on
a plane, no three of 6 ∙5 ∙ 4
which are collinear.? N= +
3!
6 ∙5 ∙ 4 ∙ 3
Solution: The polygons +
may have 3, 4, 5 or 6 4!
vertices. Thus, the 6 ∙5 ∙ 4 ∙ 3 ∙2
+
number of N possible 5!
polygons is: 6 ∙5 ∙ 4 ∙ 3 ∙2 ∙ 1
6!
N = C(6,3) + C(6,4) +
C(6,5)+ C(6,6) N= (5x4)+(5x3)+6+1
N= 20+15+7
N= 42 possible
polygons

F. Developing mastery Activity 1: Flex That

Brain!

Instructions: Find the

unknown in each item.
1. C(8,3)=
2. C(n,4)=15
3. C((8,r)=28
4. C(9,9)=
5. C(n,3)=35
6. C(10,r)=120
7. C(n,2)=78
8. C(11,r)=165
9. C(8,6)=
10. C(14,10)=

G. Finding ELABORATE The teacher will ask the

practical following questions:
application of
concepts and 1. What is Combinatorics
skills in daily combinatorics? is the branch of
living 2. What is mathematics
combination? studying the
H. Making 3. What is the enumeration,
generalization and difference between combination, and
abstractions about a permutations permutation of sets
the lesson and combinations? of elements and the
mathematical
relations that
characterize their
properties.
 A combination is a
mathematical
technique that
determines the
number of possible
arrangements in a
collection of items
where the order of
the selection does
not matter. In
combinations, you
can select the items
in any order

A permutation is an
act of arranging
objects or numbers
in order.
Combinations are
the way of selecting
objects or numbers
from a group of
objects or
collections, in such
a way that the order
of the objects does
not matter.
I. Evaluating EVALUATE Activity 2: Choose
learning Wisely, Choose Me

Instructions: Solve the

following problems
completely. (Choose a
partner.)
1. If there are
12 teams in a
basketball
tournament and
each team must
play every other
team in the
eliminations, how
many elimination
games will there
be?

2.  If there
are 7 distinct
points on a plane
with no three of
which are
collinear, how
many different
polygons can be
 possibly formed?

3. From a population
of 50 households,
in how many ways
can a researcher
select a sample
with a size of 10?

4. In how many ways

can the director of
a research
laboratory choose
two chemists from
among seven
applicants and
three physicists
from among nine
applicants?

5. In how many ways

can a person
choose four books
from a list of nine
best - sellers?

J. Additional EXTEND The Teacher will give the

activities for learners an assignment.
application or
remediation Perfect Combinations!
Study the following
situations. Then, answer
the questions that follow.

1. Determining the
top of three
winners in a
Science Quiz Bee.

2. Forming lines from

six given points
with no three of
which are
collinear.

3. Forming triangles
from 7 given points
with no three of
which are
collinear.

4. Four people
posing for pictures.

5. Assembling a
 jigsaw puzzle.

Prepared by: Checked by: Noted:

JEROME F. JIMENEZ MARITES GANITANO DR. RICO A. REYES

Student Teacher Cooperating Teacher FS Mentor