Math 10 Quarter 3: Illustrating Permutations of Objects

Math 10 Quarter 3: Illustrating Permutations of Objects

Prepared by: Jan Nicollo Alfred Dacquel

​LEARNING OBJECTIVES

The learner illustrates permutation. (M10SP-IIIa-1)​

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a. Illustrate permutations of objects.

b. List all the possible ways of a certain task or activity can be done.

c. Appreciate the importance permutations in our daily lives.

Gian invited his close friends Razodon, Zaldy, and Abdiel to his 18th birthday at Good Taste, Legarda. He prepared a special table with chairs placed in a row to be occupied by his three friends.

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Open Ended

1. List all the possible seating arrangement.

Multiple Choice

How many ways they can be seated in a row?

• 6

• 3

• 2

• 1

Open Ended

Why a shorter code is "weak", while a longer code is a "strong" personal password in a certain computer account?

Multiple Choice

It is the arrangement of all or parts of a set of objects with regards to the order of all the possible arrangements.

• Permutation

• Combination

• Statistics

• Probabiloty

Multiple Select

Permutations can be determined by _________________ .

• Listing

• Using table

• Tree diagramming

• Fundamental Counting Principle

Multiple Choice

This is use to calculate the total number of permutations in a given situation.

• Permutation

• Tree diagramming

• Listing

• Fundamental Counting Principle

Illustrative Example 1:

Suppose that you secured your suitcase using a combination lock. Then later, you forgot the 4-digit code and you can only remember that the code contains the digits 1, 3, 5 and 7.​

Open Ended

List all the possible codes out of the given digits.

Multiple Choice

How many possible codes are there in all?

• 16

• 20

• 24

• 28

Open Ended

Use the Fundamental Counting Principle (FCP) to check if the number of permutations is correct.

Solution:

​ 1st 2nd 3rd 4th

We have, 4 x 3 x 2 x 1 = 24

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Therefore, there are 24 codes in all containing the 4-digit 1, 3, 5 and 7.​

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Illustrative Example 2:

​Aling Rosa is from La Trinidad, Benguet and she really loves planting. In her garden, she is planting 6 potted plants, so how many ways can she arrange the 6 potted plants in a row?

Multiple Choice

In how many ways can Aling Rosa arrange 6 potted plants in a row?

• 720

• 702

• 270

• 207

Solution:​

Let N = 6 x 5 x 4 x 3 x 2 x 1

​ = 720

(because there are 6 choices for the 1st position, 5 choices left for the 2nd position,​ 4 choices left for the 3rd position, and so on)

​1. One of the activities of the Panagbenga Festival this year is a race competition. The participants of this race are coming from some of the different  public secondary schools in the city namely, Baguio City National High School (BCNHS), Bakakeng National High School (BNHS), Dona Aurora National High School (DANHS), Guisad Valley National High School (GVNHS), Irisan National High School (INHS), Magsaysay National High School (MNHS), Pines City National High School (PCNHS), Pinsao National High School (PNHS), Rizal National High School (RNHS) and San Vicente National High School (SVNHS). In how many possible ways can they be arranged as first, second, and third placers?

​Complete the table:

​Complete the table:

Open Ended

How did you determine the different ​possibilities in the given situation?

Open Ended

What mathematical concept or principle did you use to determine the exact number of ways in each situation?​

Open Ended

How was the concept/principle applied?​

Find what is asked in each problem:

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1. Find the total​ number of outcomes of each given situation below.

​a. tossing a coin three times

b. answering two multiple question​ with four choices

Find what is asked in each problem:

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2. How many ways 4-digit codes can be formed from the digits 1, 3, 5, 7 and 9 if repetition of digits is not allowed?

Solve the following problems individually:

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1. In how many ways you can place 9 different books on a shelf if there is enough space for only 5 books?​

Solve the following problems individually:

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2. In how many ways can 5 learners arrange themselves in a ​row for picture taking for their moving up ceremony?

Open Ended

What is permutation?

Open Ended

What are the different ways we can determine permutations?

Open Ended

What is Fundamental Counting Principle?

Open Ended

How does the concept of permutations help in formulating conclusions and making wise decisions?

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​Thank you for listening :)