This document provides teaching materials on permutations for a mathematics class. It includes examples, activities, and practice problems for students to illustrate and solve permutations of objects. The first activity asks students to find the number of possible passwords that can be created from rearranging four letters in Shayna's name for her 22 students. Later activities involve listing arrangements of different objects, finding factorials, and solving permutation problems. The document aims to help students understand and apply the concept of permutations through examples, guided practice, and assessments.
3. GUIDE CARD
Remembering define permutation
Applying give examples that illustrate permutation
Evaluating solve problems involving permutations
Valuing Makatao
Valuing show teamwork by working in pairs/group
Competency : illustrates the permutation of objects.
solves problems involving permutations
Objectives/ SubTasks :
5. •SHAYNA uses the four letters
of her nickname S,H,A, and Y
in different order to assign
computer log-in passwords
to her 22 students. Each
letter appears only once in a
password.
ACTIVITY 1
6. 1. Are there enough passwords for
Shayna’s 22 students?
2. How many different passwords
can SHAYNA create?
3. Explain how to find the number
of passwords possible if there are 6
letters available.
7. TREE DIAGRAM and LISTING METHOD
S
H
A
Y
A
H
Y
H
A
Y
Y
A
Y
H
A
H
SHAY SHYA SAHY SAYH SYHA SYAH
11. Activity 2: Drill and Practice
A. Suppose you secured your bike using a
combination lock. Later you realized that you
forgot the 3- digit code.You only remember that
the code contains the digits 1, 3, and 4.
•1. List all the possible codes out of the given
digits.
•1,3,4 - 3,4,1 – 4,3,1 – 4,1,3 – 3,1,4 – 1,4,1
•2. How many possible codes are there?
•6
12. B. In how many ways can you arrange 3
people in a row?
•1. List all the possible arrangements ( use A, B & C
in referring to the 3 people)
•ABC, ACB, BCA, BAC, CBA, CAB
•2. How many possible arrangements are there?
•6
26. DIFFICULT 1
In a room, there are 10 chairs in a
row. In how many ways can 5
students be seated in consecutive
chairs?
5!6=720
27. DIFFICULT 2
8(7)(6)(5)(4)(3)(2)(1) = 8!
= 40,320.
The simplest protein molecule in biology is called
vasopressin and is composed of 8 amino acids that are
chemically bound together in a particular order. The order
in which these amino acids occur is of vital importance to
the proper functioning of vasopressin. If these 8 amino
acids were placed in a hat and drawn out randomly one by
one, how many different arrangements of these 8 amino
acids are possible?
28. DIFFICULT 3 a
4!2!2!2!2!=384
Four married couples have purchased
eight seats in a row for a football
game. In how many different ways
can they be seated if:
a. each couple is to sit together.
29. DIFFICULT 3 b
4!4!2!=1152
Four married couples have purchased eight
seats in a row for a football game. In how
many different ways can they be seated if:
b. all men are to sit together and all the
women are to sit together.
30. DIFFICULT 3 c
4!4!2!=1152
Four married couples have
purchased eight seats in a row for a
football game. In how many
different ways can they be seated
if:
c. all men are to sit together.
31. DIFFICULT 3 d
4!4!2!=1152
Four married couples have purchased
eight seats in a row for a football game.
In how many different ways can they
be seated if:
d. the men and women are to sit in
alternate sits.
33. 1. How many four- digit numbers can be formed from the numbers
1, 3, 4, 6, 8, and 10 if repetition of digit is not allowed?
2. In how many ways can 5 people arrange themselves in a row for
picture taking?
3. In how many ways can you place 9 different books on a shelf if
there is space enough for only 5 books?
4. List down the possible arrangements of a 4 - digit number using
the digits 0,1, 2, and 3 without repetition and no other number
should start with 0 . Check your answer using FCP.
5. How many four- digit numbers can be formed from the numbers
1, 3, 4, 6, 8, and 9 if repetition of digit is not allowed?
