nCr and nPr 6(5m) @ xvnjcke的部落格

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nCr and nPr 6(5m)

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please help me 5 questions. I need steps. (solution at the bottom) thank you. 5 marks 1. 10 horizontal lines and 15 vertical lines are intersected. How many rectangles can be formed? 2. In a badminton tournament, any 2 players must play against each other twice. However, a player was quit after playing 4... 顯示更多 please help me 5 questions. I need steps. (solution at the bottom) thank you. 5 marks 1. 10 horizontal lines and 15 vertical lines are intersected. How many rectangles can be formed? 2. In a badminton tournament, any 2 players must play against each other twice. However, a player was quit after playing 4 matches due to injury. If a total of 60 matches were played finally, how many players were there originally? 3. Peter plans to deliver 12 packages to 12 different spots. (a) 3 packages will be delivered to 3 spots in the same district, so they will be delivered successively. How many delivery sequences does he have now? (b) Apart from the 3 packages mentioned in (a), there are 4 packages to be delivered to 4 spots in another district successively. How many delivery sequences does he have now? 4. Gordon has 10 game discs, where 6 of which are tactical games and 4 are action games. He has a disc rack which can hold 6 game discs. If Gordon selects 4 tactical game discs and 2 action game discs out of 10 game discs to be put on the rack, how many permutations are there? 5. Given 2 x 37 x 47 x 67 x 97 = 22 603 522. How many positive even factors of 22 603 522 are there? Hint: Is 2 x 37 a positive even factor? Is 2 x 47 x 67 a positive even factor? Solutions: 1. 4 725 2. 9 3. (a) 21 772 800 3. (b) 725 760 4. 64 800 5. 16 更新: 6. There are 3 different types of publications, including 4 different news journals, 5 different entertainment magazines and 6 different comic books. (a) If 3 different publications are picked, how many combinations are there? 更新 2: 6. (b) If 3 publications are picked, where some of them are of the same type, how many combinations are there? (c) If 3 publications are picked, where at least one of them is a news journal, how many combinations are there? Solutions: 6. (a) 120 (b) 335 (c) 290 更新 3: 7. There are 12 different plants in the balcony and 5 of them are cactuses. The plants are now arranged in a row. If cactuses cannot be placed at the two ends, how many permutations are there? Solutions: 152 409 600 更新 4: 8. There are 9 different books. How many ways to arrange the books in a shelf with 3 racks, such that there are 3 books on each rack? Solution: 362 880 更新 5: 9. In a test paper, there are 10 MC questions. Each question has 4 choices. If 1 choice must be selected for each question, how many arrangements are there to answer the paper? Solution: 1 048 576 更新 6: 10. There are 10 seats in a row in a waiting room. There are 6 people in the room, given that there are 3 sisters. The sisters must sit next to each other. Find number of different ways can the group be seated. Solution: 10 080 更新 7: 11. Below shows the distribution of the number of librarians of a school. Mr. Chan plans to select 6 outstanding ones for the best librarian awards. Find no. of combinations if selecting a student from each form and there are at least 1 boy and 1 girl. 更新 8: (B=Boy and G=Girl) S1 - 4B + 8G S2 - 7B + 8G S3 - 10B + 12G S4 - 2B + 6G S5 - 3B + 4G S6 - 1B + 3G Solution: 830 064