MATH 10
COMICS ON
COUNTING
TECHNIQUES
MINERVINA V. JIMENEZ
JOHN WILLIAM B. PONCE
MODULE 1 – Solving Problems Involving
The Fundamental Counting Principle
I. Objectives:
1. Solve problems involving the Fundamental
Counting Principle (FCP).
2. Fill in the appropriate words or quantities to
complete the dialogues included in the comics of
solving problems involving FCP.
II. Guide Questions: (Formative Assessment)
1. How do you solve problems involving the
Fundamental Counting Principle (FCP)?
2. How do you fill in the appropriate words or
quantities to complete the dialogues included in the
comics of solving problems involving FCP?
III. Discussion:
Do you know how to count systematically?
Counting possibilities existing in real-life
situations involving the basic counting technique
called the Fundamental Counting Principle (FCP)
will be laid here in the form of comics. The concept
of FCP will help you draw conclusions on such
situations and eventually make wise decisions on
them. Let us then refresh our minds on this
counting technique.
The Fundamental Counting Principle (FCP) states
that suppose there are p ways for an event to occur,
q ways for a second event to occur independently of
the first, r ways for a third to occur independently
of the first two and so on, then the total number of
ways for the three events/actions to occur in
succession is p x q x r…
IV. Example
MODULE 2 – Solving Problems Involving
Permutations
I. Objectives:
Solve problems involving permutation. (M10SPIIIb-1)
Specifically, it aims to:
1. Solve problems involving permutations.
2. Fill in the appropriate words or quantities to
complete the dialogues included in the comics of
solving problems involving permutation.
II. Guide Questions: (Formative Assessment)
1. How do you solve problems involving
permutations?
2. How do you fill in the appropriate words or
quantities to complete the dialogues included in the
comics of solving problems involving permutation?
III. Discussion:
Solving problems involving permutation as a
counting technique will be discussed and unveiled
using comics strips. Preparatory to this, let us revisit
the concept of permutation and the formulae
pertaining to it.
Permutation is a counting technique which pertains
to the number of different possible arrangements of a
set of objects where order matters.
The permutation of n objects taken all at a time is P(n,n) = n!
The permutation of n objects taken r at a time is P(n,r)
= n!/(n-r)! , n > r.
The number of distinguishable permutations of n
objects, where m objects are alike, n objects are alike, p
objects are alike and so on called the distinguishable
permutation is P = n!/(m!n!p!…) The circular permutation of
n objects is P = (n-1)
IV. Example
MODULE 3 – Solving Problems Involving
Combinations
I. Objectives:
Solve problems involving permutation and
combination. (M10SPIIId-e-1)
Specifically, it aims to:
1. Solve problems involving combination;
2. Fill in the appropriate words or quantities to
complete the dialogues included in
the comics of solving problems involving combination.
II. Guide Questions: (Formative Assessment)
1. How do you solve problems involving
combinations?
2. How do you fill in the appropriate words or
quantities to complete the dialogues
included in the comics of solving problems involving
combinations?
III. Discussion:
The problems on combination will be unveiled
using comic strips. In here, you will fill in the needed
words to complete the thought or quantities to solve
the problems. First, let us recall concepts and formulas
on combinations.
The number of ways of choosing from a set of objects or
persons when the order is not important is called
combination.
The number of combinations of n objects taken r at a
time is given by
C(n,r) = , n ≥ r.
Now, are you ready to solve problems involving
combinations introduced through comic strips?
Come on! Sit back, relax and enjoy reading the comics…
IV. Example
Part II. Solve the following problems below.
Show your solution so as to get full credits.
1. In how many ways can 5 students be seated in a
round table of
5 seats if 2 of them insist on
sitting beside each other?
2. If a combination lock must contain 5 different
digits, in how many ways can a code be formed from
the digits 0 to 9?
3. A license plate consists of three letters and
three numbers. If the letters are vowels only, and
the number choices for each digit will only be odd
numbers, how many different license plates can be
made if no letter and number is used more than once?
4. Mila is transferring to a new house. She has a
collection of books but she cannot take them all
with her. In how many ways can she select 5 books
out of 12, and then arrange these books on a shelf
if there is a space enough for only 5 books?