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Combinations In this lesson, you are expected to illustrate combination of objects and differentiate permutation of n objects taken r at a time. When the order does not matter, it is a Combination. When the order does matter it is a Permutation. Combination is the collection of objects in no particular order. The order of objctsis not important and can be placed in any order. Example 1: RV, Rhian, Markson, Arwin, Kasey are the top 5 students of Mrs. Estrada in Mathematics class. Mrs. Estrada must choose 2 out of 5 of her best students to become school representative in Math Olympiad. In how many ways can she do that? Solution: Illustrating of possible combination we have: RV and Rhian --- RV and Markson- RV and Arwin- RV and Kasey--. Rhian and Markson In the given example we COCO VOU AWN Rhian and Arwin-- have 10 ways Rhian and Kasey- Markson and Arwin-- Marson and Kasey Arwin and Kasey 10 Using the combination of n objects taken r at the time, we have 5 top students in Math class, so n = 5 Selecting top 2 students, so n = 2 C (n , r) or n Cr = n! 5 ! 5 x4 x3! 20 = 10 ways (n-r)!r! (5-2)12! 3! 2x1 Example 2: Determine whether a given situation is a combination or not. 1. Winning in a running event. (arrangement is important because of the places) 2. Selecting 5 people to form a team. Answer: Combination (arrangement is not important) 3. Unlocking a phone using a passcode. Answer: Not Combination (order matters) 4. Drawing a set of 6 numbers to win a 6/45 lottery. Answer: Combination (order not matters) 5. Five badminton players chosen from a group of nine. Answer: Combination, because you are just going to select 5 badminton players from a group of nine. Therefore, the order in selecting is not important.A. LET'S PRACTICE! Direction: Determine whether the given situation is a combination or not. Write C if it is a combination and NC if it is not a combination. 1. Different sets of 5 cards formed from a standard deck of 52 cards. 2. A die is rolled thrice. 3. Ate Neng arranged 6 potted plants in a row. 4. Answering 3 out of 8 essay questions test. 5. Seven front liners stand in row for claiming the snacks. 6. In how many ways can a coach choose three swimmers from among five swimmers? 7. How many 4 digit numbers can we make using the digits 2, 5, T, and 9 without repetitions? 8. Acommittee including 4 boys and 5 gins is to be formed from a group of 8 boys and 10 girls. How many different committee can be formed from the group? 9 . How many triangles can you make using 7 non collinear points an a plane? _10. How many 5 letter words can we make using the letters in the word LIBERTY without repetitions? B. TEST YOURSELF! Direction: Determine whether the given situation is a combination or not. If it is not, rephrase the situation or task to make it a combination. 1. Choosing six officers from the class. 2. Selecting 3 balls from a box containing 6 red balls and 4 blue balls. 3. Eight workers are assigned to 8 differentjobs. 4. Find the number of ways a president, a vice president, and a secretary can be chosen from among Aaron, Blessie. Carmi, Darius. and Elvie. 5. A committee of 4 members chosen from 6 women and 5 men. C. Find each value: 1. C(33) = 2. C(72) = 3. C(85) -C(7,3) = 4. C(24,21) = 5. 012,8) =