LEARNING ACTIVITY SHEET
ACTIVITY 1: Recalling Factorials
Illustrating factorials is a prerequisite skill in permutation. In this activity, the learners will recall factorials.
Ask the learners to give the answer by finding factorial of the following:
1.
2.
3.
4.
5.
3!
4!
5!
6!
8!
ACTIVITY 2: What’s the Passcode?
Arrangement of objects matter. In similar way, we have to assign particular arrangement of objects for
some purposes. For instance, we use screen lock passcodes to keep our privacy and security just what we
do in our mobile phones or gadget.
Suppose you are about to unlock your screen but you accidentally forget the exact arrangement of the
4-digit code. What you remember are the numbers 1, 2, 3, and 4 but you are not sure of the exact
arrangement of these numbers. Can you still recover the passcode? How will you do this?
Questions:
1.
2.
3.
4.
5.
Initially, what did you do to recover the passcode?
How many possible attempts can you do before you can unlock the screen?
What are those possible passcodes that you can make out of the numbers 1, 2, 3, and 4?
What process did you do to come up with those digits?
Do you think arrangement of objects is important? Why?
ACTIVITY 3: What’s in this Lesson?
Determining the different possibilities of an event requires counting. There are four techniques in
counting events namely making a table, tree diagram, systematic listing and fundamental principle of
counting.
Making a table is a technique where values or different possibilities are tabulated.
Tree diagram is another technique which uses line segments originating from an event to an outcome.
This is a picture of all possible outcomes when an event is unfolded.
Systematic listing is a counting technique that involves complete list of all possible outcomes.
Fundamental counting principle is a counting technique in which if two events are independent and one
event occurs in a ways, and the other event occurs in b ways, then, these events occur in ab ways.
Example:
There are 4 cyclists in a race. In how many ways will they be arranged as first, second, and third
placers?
To answer this problem, we can use any of the four counting techniques mentioned above.
Making a table
Number of Cyclists
4 (A, B, C, D)
Possible Arrangements
No. of Arrangements
3 cyclists at a time (for first, second, third):
24
ABC, ABD, ACB, ACD,
ADB, ADC, BAC, BAD,
BCA, BCD, BDA, BDC,
CAB, CAD, CBA, CBD,
CDA, CDB, DAB, DAC,
DBA, DBC, DCA, DCB
Systematic listing
There are only four cyclists: A, B, C and D. There are four cyclists to choose from for the first place,
three cyclists to choose from for the second place and two cyclists to choose from for the third place.
The actual list of all possible arrangements are ABC, ABD, ACB, ACD, ADB, ADC, BAC, BAD,
BCA, BCD, BDA, BDC, CAB, CAD, CBA, CBD, CDA, CDB, DAB, DAC, DBA, DBC, DCA, DCB.
Therefore, there are 24 possible arrangements.
Fundamental counting principle
first placer
second placer
third placer
Processing Questions:
1. Describe the arrangement of cyclists as first, second, and third placers? Is the order or arrangement
important?
2. Is the list of possible arrangements of cyclists that are made is complete and actual?
3. What do you call each possible arrangement of cyclists?
ATTACHMENT
Module 1 - Lesson 1: Permutation of Distinct Objects
Permutation refers to the different arrangement of objects in a definitive manner. The order of the objects
is important. There are two types of permutations. These are permutations of objects in a line and
permutations of objects in a circle. Permutation of distinct objects and permutation of non-distinct objects
are the two kinds of permutations of objects in a line. But in this lesson our focus is permutation of distinct
objects.
What is permutation of distinct objects?
Permutation of distinct objects refers to the different arrangements of distinct objects in a line. It is the
different arrangements when no objects are identical or the same.
Examples:
1. Arranging 4 different potted plants in a row
- What makes this a permutation of distinct objects is that, 4 different potted plants are distinct objects
and are arranged in a line.
2. Getting the possible arrangements of letters of READ
- The four letters in READ are all distinct letters and are arranged in a line.
3. Choosing president, vice president, secretary and treasurer from 12 members in a club.
- A president can’t be a vice president or a secretary or a treasurer at the same time so meaning, 4
different officers are to be chosen from 12 members.
ACTIVITY 4: Arrange Me Accordingly
Situation/
Activity
No. of
Objects
Example 1:
Arranging
3
different pictures
of cultural heritage
in the province
Marinduque for a
photo exhibit.
Discussion of the Possible Arrangements
3 pots at a time:
3
Using tree diagram:
With the use of Fundamental Counting Principle:
Thus, there are 6 possible arrangements of 3 different pictures of
cultural heritage in Marinduque.
4 potted plants at a time:
Example 2:
Arranging 4
different potted
plants in a row label
Plant A, B, C and
D.
4
The possible arrangements are:
ABCD, ABDC, ACDB, ACBD, ADBC, ADCB, BCDA, BCAD,
BDAC, BDCA, BACD, BADC, CDAB, CDBA, CABD, CADB,
CBDA, CBAD, DABC, DACB, DBCA, DBAC, DCAB, DCBA
With the use of Fundamental Counting Principle:
Therefore, there are 24 possible arrangements of 4 potted plants in a
row.
Example 3:
Electing a
Mathematics club
president, vicepresident and a
secretary from 10
members
3 students at a time:
10
This is different from other possible results, like:
President- Adrian Frias
Vice-President- Jerovy Caluag
Secretary: Charmel Vizarra
(Note: It’s hard making a list of all possible arrangements when the list
is long.)
The number of possible outcomes for the position:
President - 5 possible choices
Vice President - 4 possible choices
Secretary – 3 possible choices
With the use of Fundamental Counting Principle:
5 x 4 x 3 = 60
There are 720 possible ways of electing Mathematics club President,
Vice President and Secretary.
Anagram is a word or phrase created by rearranging all the letters of a
certain word, and these letters must be used only once.
Example 4:
Getting the possible
arrangement
of
letters that could be
the anagram of the
word READ.
5
Since we are getting the possible arrangements of letters of READ that
has meaning, then the possible words that could be formed are DEAR
and DARE.
Thus, there are only 2 possible arrangements.
ACTIVITY 5: It’s My Turn
Identify which among the following situation illustrates permutation of distinct objects. Write P if the
situation shows permutation and NP if does not show permutation.
1. Shoe is the anagram for hose.
2. She arranges 6 different potted plants in a row.
3. The saleslady displays 5 the same rubber shoes on the display rack.
4. The letters of MATH can be arranged into 24 ways.
5. The teacher selects 2 leaders from the 5 members in the group with no particular order.
6. The librarian arranges 5 Mathematics books, 2 English book and 3 Science in a shelf.
7. The cashier opens a vault with different digits of combination lock.
8. The customer chooses 2 vegetable dishes from a menu of 6.
9. Mrs. Cruz can hang her 3 different photo frames in a row on the wall in 6 ways.
10. Permutation of distinct objects is the different arrangement of distinct objects in a line.
ACTIVITY 6: Situationalysis (Situation – Analysis)
Direction: Read and understand the problem below and answer what is asked in the problem.
Vice Ganda is a well-known concert artist. Suppose he is planning to have a concert tour in four cities –
Baguio City, Cebu City, Davao City, Puerto Princesa City and Olangapo City.
Questions:
1. Is it possible to list and count the possible ways he can arrange his tour schedules for the concert tour?
2. What is the easiest counting technique that you can use to determine the possible arrangement of his
tour schedule?
3. In how many ways can he arrange his possible schedules for the concert tour?
Assignment
Follow-up:
Directions: Rearrange the letters of the words below and find the possible arrangement of these letters that
could be the anagram of these words. (Hint: Body Parts)
1. ONES
2. CAFE
3. INCH
4. FRINGE
5. IMPART
Advance Assignment:
What are non-distinct objects? Is it possible to find the permutation of non-distinct objects? How?