A. Read the problem and answer the questions below, (illustrates the permuta object. MIOSP-IIIa-1) There are 7 friends who decided to go to Sampaloe Lake for a ride, however, there are only 4 available bikes, While waiting, they take a picture in a row as a souvenir. They also buy food from the stalls. They have 3 choices such as thaw-thaw, queck-queck, and hotdog on sticks and 2 kinds of beverages (buko juice and palamig). While eating they sit on the view deck in a circular form, having so much fun. They play a game of arranging all letters found in "Sampaloc Lake" like SAMPALOC LAKE and get a new name related to it such as CLAKE, a barnacle goose. I Illustrate the possible ways of paring the food with beverages by using a tree dingram, systematic listing, and table. 2. In how many different ways can they arrange to give everybody a chance to experience the ride 3.In how many ways can they arrange themselves in a row for picture taking? 4. In how many ways they can be seated on the view deck? 5.Using the letters in SAMPALOCLAKE, how many distinguishable permutations are there? B. Solve the following problems. Choose the letter of the best answer. (solves problems involving permutations, MIOSP-IIIb-1) 1. A store manager wishes to display 8 different brands of shampoo in a row, How many ways can this be done? A. 40,320 B.38,630 C.29,520 D.35,420 2. A man flips ten coins among his ten children. The coins are two one-centavo coins, three live- centavo coins, and five twenty-five centavo coins. If each item is to get one coin, in how many ways can the children share the coins? A. 1,230 B.1,540 C. 2,520 D. 1,870 3. A bracelet needs 10 chains of different colors. In how many ways can the chains be arranged or joined to form a bracelet? A.225,530 B.300,640 C.325,120 D. 362, 880 4. Mar, Marlon, Marvin, Martin and Marco decided to go to SM Dasmariflas, Each of them has their own motorcycle. Upon arriving at the parking lot, there are 7 available parking spaces. In how many different ways can their motorcycle be parked? A 1,550 B. 2,520 C. 1,820 D. 2,320 5. How many different ways can a President and a Vicepresident be selected for classroom officers if there are 30 students in a class? A. 870 13.750 C.520 D.850 B. C. Answer the following.(lustrates the combination of objects. (M10SP-IIIe-1) You want to surprise your mother on her birthday by preparing a fruit salad. You went to Tagaytay City market to buy ingredients (pineapple (P), papaya (PA), banana (8), and buko (BU)). Due to limited budget and you still want to give your mother a present, you are opted to buy only 3 different fruits. List all possible combinations. 2. 3. 5.How many possible combinations