answer the questions

\fActivity 2. Arrange Me Directions: Study the following situations and give what is asked. Write your answers on the space provided 1. Hillary bought a new house in the city. She wanted to have flowering plants in front of her new house. She bought 8 flowering plants and wish to arrange 4 of the plants in a row. a. How many possible ways can she arrange her flowering plants? b. How did you determine the possible number of arrangements that Nina can do to her flowering plants? 2. An ATM PIN code have 4 digits in a specific order. It contains digits between 0 to 9. a. How many different PIN codes can be made from the given digits if one digit may only be used once? b. How did you determine the number of PIN codes made? 3. Given the name DAVE. a. In how many ways can you arrange its letters, 3 at a time? b. How did you find the possible ways to arrange the letters? Activity 3. Find Me in The Box Directions: Solve the given problem then choose your answer among the choices in the box below. Write the letter of your choice on the space provided before each number. If you cannot find the answer in box, you may write your answer. Write the solution in a separate sheet of paper. a. 126 b. 15, 120 c. 336 d. 32,760 e. 1,320 1. There are 12 finalists in a dance competition. How many ways can gold, silver and bronze medals be awarded to them? 2. In your class, there are 15 qualified candidates to be elected as classroom officers. If you are going to ist choose a President, Vice-President, Secretary, and Treasurer among the qualified candidates, in how many ways can you select each position? 3. Eight people join the Food Making contest. How many ways can a Ist and and 3id placer be awarded? 4. How many ways can 4 Math books and 5 English books be put on a shelf if all the Math books and the English books have to be put together? 5. In how many ways can Alexa place 9 different books on the shelf if the space is enough for only 5 books?Where you able to answer all the given problems? How do you feel? Just relax because more exciting situations are waiting for you. Activity 4. I'm Different Directions: Study the given situations below and give what is asked. A. Answer the questions completely. Write your answers on the space provided. 1. Mavis, Tina, Roselle, Lyka and Anje are best of friends. While walking in a park, they saw a photographer taking photos. So, they decided to take a group photo to have a souvenir . a. In how many ways can the photographer arrange them for a picture taking? b. How did you determine the number of possible ways in the problem? 2. Given the word MATH. a. In how many ways can you arrange the word at all time? b. How did you find the possible ways to arrange the letters of the word? B. Solve the problem accurately. Place your answer in the box provided for each item. Write your solutions in a separate sheet of paper. 1. Bernardine wants to arrange her Matin Mathematics, English, Science and Filipino Filipino books on a shelf in her room. In how many ways can she do it? English 2. In how many ways can 7 people stand in a queue? 3. How many ways can the letters of the word BEAUTY be rearranged? 4. How many 3-digit numbers can you make using the digits 1, 2 and 3? 5. In how many different ways can the letters of the word JUDGE be arranged to form other words with or without meanings? Notice that in the activity, all objects to be arranged are all distinct. Suppose some of the objects to be arranged are not FACT. distinct, that is, some are identical, how do we find the possible ways of the permutation? Find out as you do the next activity.Activity 5. I Am Unique! Directions: Study the given situations below and give what is asked. A. Read, analyze and solve each problem carefully. Write your answers on the space provided. 1. Nash received 8 different awards which include ribbons, certificates and medals during his graduation day. He received 3 golds, 2 silvers and 2 bronze. a. What medals are identical? . b. How many ways can he display his awards? c. How did you determine the possible ways in the problem? 2. Arjel wanted to find the number of permutations of the letters of the word ASSASSIN. a. How many letters are there in the word ASSASSIN? b. How many letters are alike? c. How many distinguishable permutations with all the letters of the word have? d. How did you determine the possible ways in the problem? B. Complete the table below to find the number of permutations with the letters of the given words and then answer the questions that follow. Write the values in the appropriate columns. Write n/a if no values applicable. Given Word n P b Answer 1. PERMUTATION 2. BANANA 3. MATHEMATICS 4. BILLIONAIRE 5. BALLISTICS 6. CHEESE 7. WORKSHEETS 8. REFERENCE 9. MEMORIES 10. FURTHER Questions: a. How did you determine the different ways of the given word in each item? b. What pattern did you use in finding the ways of the given words?C. Answer each item completely then encircle the letter of your answer. Write your solutions in a separate sheet of paper. 1. How many distinguishable permutations exist in the word TENNESSEE? a. 8,073 b. 7,308 c. 3,780 d. d. 3,078 2. How many different words with or without meaning can be formed from the word SUCCESS? a. 420 b. 402 c. 240 d. d. 204 3. How many permutations can be formed from the word PHILIPPINES? a. 1, 108,800 b. 1,100,880 c. 1,010,880 d. 1,001,088 4. How many different words (real or imaginary) can be formed using all the letters in the name WENDELL? a. 6,021 b. 2, 106 c. 1,602 d. 1,260 5. In how many ways can the letters of the word MATHEMATICS be arranged in a row? a. 4,998,600 b. 4,989,600 C. 4,969,800 d. 4,699,008 How did you find the activity? I'm sure it is easy for you. Let's find more exciting cases of permutation. Have fun! Activity 6. Merry Go Round Directions: Study the given situations below and give what is asked. A. Read, analyze and solve each problem carefully. Write your answers on the space provided. 1. Ira, Aloy, Prince, Radz, Dyrill, and John are in a restaurant. They are going to sit around a circular table. a. In how many ways can they be seated around the table? b. How did you calculate the possible ways?_2. A, B, C, D, E, F were late in attending a party. As they enter the lawn there's only one circular table with 5 chairs available so two of them will sit together. a. In how many ways can they be seated such that A and B must always sit together? b. How many ways can they be seated such that C and D must not sit together? c. How did you determine the number of ways that they can be seated in items a and b? B. Solve the problems in Column A and match the answers in Column B. Write the letter of your answer on the space provided. Write your solutions in a separate sheet of paper. Column A Column B 1. Anna and Rita want to plant some flowering plants around a. 362,880 a circular walkway. They have eight different flowering b. 720 plants. How many different ways can the flowering plants c. 1,440 be planted? d. 120 2. In how many ways can 10 people be seated in a round table? a. 6 3. How many ways in which 8 men be arranged around a table so that 2 particular men must always sit together? 4. How many ways can 4 people be seated around a circular table? 5. In how many ways can 6 married couples be seated around a circular table? GREAT! Were you able to solve all the problems correctly? I hope you did it right! Now, apply what you have learned to the next activity. Activity 7. Do You Remember Me? Directions: Solve the given problems on permutation accurately. Write your solutions in a separate sheet of paper. 1. In how many different ways can the 4 positions in a relay team be filled by 10 qualified athletes? 2. How many ways can we order 7 computers if we have only space for 4? 3. How many ways can 9 people be seated at a round table? 4. If there are 10 people and only 6 chairs are available, in how many ways they can be seated? 5. In how many distinguishable permutations are possible with all the letters of the word STATISTICS? 6. Mrs. Villar wants to assign 6 different tasks to her 6 students. In how many ways can she do it?7. How many possible bracelets can Hanna make if she will use all the 10 different beads she has? 8. How many words can be formed with the letters H,E, A, R,T where "E" and "A" occupy the end places? 9. There are 6 people who will sit in a row but out of them Rachel will always be at the right of Sol? How many arrangements can be done?_ 10. License plates are formed using three letters followed by a four - digit number without repetition of either letters or digits. ABC 1234 Zero may be chosen as the first digit of the number. How many license plates can be formed under this pattern? Activity 8. Share It! Directions. Work in pair to do the tasks in this activity. You may contact your chosen partner through phone calls, messaging or video calls. Write your outputs in a clean sheet of paper. Tasks: 1. Each of you will identify a real-life situation that involves permutations and explain its relationship to permutations. 2. Create a problem involving permutations based on the identified situation. 3. Exchange the problem with your partner then solve it. 4. Write your complete solution in a clean sheet of paper. 5. Check the answer of your partner if correct. If not, explain how to get the correct answer How were the activities done so far? Were you able to solve all the problems? I hope you understand everything SM about solving problems on permutations. Here's how your outputs be rated.Remember: . If any event can occur in m ways and after it happens in any one of these ways, a second event can occur in ways, then both events together can occur in m x n ways. . n - Factorial is the product of the positive integer n and all the positive integers less than n. That is, n! = n x (n-1) x (n-2) x (n-3)... (3) x (2) x (1). . Permutation is an arrangement or listing in which order is important. Case 1. The permutation of n objects taken r at a time is P(n, r) = Case 2. The permutation of n objects taken all at a time is P(n, n) = n!, n = r Case 3. The number of distinguishable permutations of n objects, where p objects are alike, q objects are alike, r objects are alike and so on is P = - p!qir! ... Case 4. the permutation of n objects arranged in a circle is P = (n-1)! Reflection In this activity, I learned that