VI. PROBLEM SOLVING. Read and analyze the problem below. Answer the following questions that follow.

You need to form a team with 5 members from a group of 12 ML players in your zone to compete for the barangay-based Mobile Legends Competition. How many different teams can be made?

1. What is asked in the problem?

2. What are given?.

3. What combinatorics method shall be appiied, permutation or combination?

4. Solve the problem. Show your solution.

5. How many different teams can be made? State your answer in a sentence.

VII. Which combinatorics is illustrated in the combination of meals, permutation or combination? Defend you answer.

VIII. SELECTION. Read the instances or scenarios given below. Write P if the given item illustrates a permutation but write NP if not.

1. choosing three songs to sing for the grand finals of a singing contest

2. selecting a president, vice president and a secretary in your class

3. designating a plate number for a vehicle

4. arranging four guests to sit around a table

5. selecting five players to play a 5v5 online game battle.

6. deciding on three dishes to cook for your mother's bithday

7. choosing five adult volunteers to form a Covid19 Patrol Group

8. assigning the first five players in an official basketball game

9. choosing three leaning modules to accomplish in a day

10. forming four letter arrangements from the word CORONAVIRUS

11. choosing three toppingsin your piZza order

12. assigning the members of the school's editorial board

13. arranging 45 students for a group picture

14. selecting five songs to play before going to sleep

15. MEATS, STEAM, MATES, TAMES

IX. MULTIPLE CHOICE TEST. Read and select the letter of the correct answer.

1. Which of the following is/are characteristics of permutation?

A. Order is relevant.

B. It is more on arrangement.

C. It refers to an ordered set.

D. All of the above

2. What is the result of 3! + 4!?

A. 6 B. 24 C. 30 D. 5040

3. What is the value of 5! ?

A. 5 B. 20 C. 120 D. 240

4. How many arrangements are possible for the permutation of the word ILOCOS?

A. 120 B. 360 C. 720 D. 2520

5. When will the value of permutation be equal to 1?

A. when n =r

B.when n = r = 1

C. when (n - r) =1

D. when r= 0

6. What is the value of P(4, 1)?

A.1 B. 4 C. 6 D. 24

7. Which of the following mathematical statements is CORRECT?

A. P(3, 2) = 1

B. P(6, 6) = 0

C. P(4,2) = 2

D. P(4,0) = 4

8. Which of the following instances illustrates permutation?

A. grouping 4 students for theperformance task

B. drawing 3 marbles in a box

C. assigning password for your phone

D. selecting students to form a committee

9. In how many ways can a president, a treasurer and a secretary be chosen from among 7 candidates?

A. 420 B. 210 C. 105 D. 60

10. In how many ways can 4 students be seated in a circular table?

A. 1 B. 4 C. 6 D. 24

11. How many four-letter arrangements, with or without meaning, can be made from the word "TALE" if repetition is allowed?

A. 4 B. 16 C. 64 D. 256

12. A zip code contains 4 digits. How many different zip codes can be made with the digits 0-9 if no digit is used more than once and the first digit is not 0?

A. 4,356 B. 4,365 C. 4,536 D. 4,635

13. A photographer is taking the picture of a group of students composed of Osmer, Kent, Phillip, Alexalyn and Yvette. Find the number of ways they can be arranged if Osmer and Yvette refuse to stand next to each other.

A. 48 B. 72 C. 120 D. 210

14. How many three-letter arrangements can be made from the word PHOENIX, if repetition is not allowed?

A. 60 B. 115 C. 120 D. 210

15. Find the value of n in nP3 = 504

A. 5 B. 7 C. 9 D. 11

X. Directions: Solve each problem involving combination. Choose your answer on the choices given above.

a. 119,700

b. 529,200

c. 4,512

d. 350

e. 1,221,759

f. 700

g. 31,360

h. 324, 632

i. 15, 960

j. 8,008

1. A group of five students is to be chosen from a 45-member

class to represent the class on the student council. How many ways can this be done?

For numbers 2-4, There are 15 females and 20 males in a grade 10 class. The principal wishes to meet with a group of 5 students to discuss about graduation.

2. How many selections are possible?

3. How many selections are possible if the group consists of two females and three males.

4. One of the female students is named Anna. How many five-member selections consisting of Anna, one other female, and three males are possible?

5. In how many ways can a committee of 5 be formed from 5 juniors and 7 seniors if the committee must have 3 seniors?

6. From a standard deck of 52 cards, how many 5 cards having exactly 3 aces and 2 others can be dealt.

7. In how many ways can 6 vacancies be filled with either 3 or 4 more among those employed if there are 9 men applicants and 7 women applicants

8. The llocos Sur Basketball Team plays 10 games during the season In how many ways can it end the season with 5 wins, 4 losses, and 1 tie?

9. If eight people eat dinner together, in how many different ways may 3 order pinakbet, 4 order dinengdeng, and 1 order fried fish?

10. A group of 4 adults and 3 children are to be formed from 8 adults and 5 children. How many possible groups are there?