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sson 8 Mathematics of Data Management MDM4 Key Questions Save your answers to the Key Questions in your Course Journal or e-Journal. Total: 22 marks 29. How many ways can you arrange the letters of the word "MATHEMATICS"? Show your calculations. (3 marks) 30. An office consists of seven men and four women. For each of the following questions, show your calculations. (7 marks total) a) How many ways can their manager choose a hiring committee of three staff from this office? (2 marks) b) How many of these committees will contain at least one man? Use the indirect approach to find the answer. (3 marks) c) How many of these committees will contain exactly one woman? (2 marks) 31. A pharmacist uses five separate weights: 1 g, 2 g, 4 g, 8 g, and 16 g. If the pharmacist can combine these weights to create new weights, how many different weights are possible? Show your calculations. (6 marks) 32. At an alternative learning school, a group of 48 students enrolled in mathematics, French, and physics. Some students were more successful than others: 32 passed French; 27 passed physics; 33 passed mathematics; 26 passed French and mathematics; 26 passed physics and mathematics; 21 passed French and physics; and 21 passed French, mathematics, and physics. How many students passed one or more of the subjects? Solve the question using the inclusion-exclusion principle. Show your calculations. (6 marks) Now go on to Lesson 9. Remember, you do