Question

Can you please solve all parts of this problem. i will rate you!

Question 6 (10 marks) (i) After the exam, the following 9 people will join us to celebrate: (Darth Vader, Luke Skywalker; Princess Leia; Han Solo; Chewbacca; Rey; Finn; Kylo Ren, and Supreme Leader Snoke). At the end of celebrations, 5 of them stand in a row for a picture. (Clearly describe your answer to each part) In how many ways can this be done if "Han Solo" is to be in the picture? 12 marks] In how many ways can this be done if neither "Darth Vader" nor "Supreme Leader Snoke" are in the picture? [2 marks] a. b. c. In how many ways can this be done if "Rey" and "Finn" are in the picture, but not standing next to each other? [2 marks] Which one of them is your favorite character? [1 mark] d. (ii) Find the number of permutations of the letters in the word COEFFICIENT. [3 marks]

Answer 1

the exam, the 9 people will join us to celebrate. (Darth vader Luke Skywalker Princess Leia. in the first part it says that Han sola should be in the picture that means one of the member among the five is already Han solo. So any 4 in the rest of the 8 will join in the picture. a) Han solo The number of ways the other 4 is to be arranged can be given with the formula. n_p_r = n!/n - r! Here the number of people Left one n = 8 and the number of spaces, r = 4. Hence 8_p_4 = 8!/(8 - 4)! = 8 times 7 times 6 times 5 = 1680 ways. (b) Here it means that 2 of them wouldn't be in the picture any ways. Hence any 5 from the remaining of would be in the picture. The number of ways that can happen can be given with the above formula 7p_5 = 7!/(7 - 5)! = 2520 ways.