IE111_F09_HW02_soln - IE 111 Fall Semester 2009 Homework#2...

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IE 111 Fall Semester 2009 Homework #2 Solutions Question 1 An order for a personal digital assistant can specify any one of five memory sizes, any one of three types of displays, any one of four sizes of a hard disk, and can either include or not include a pen tablet. How many different systems can be ordered? Answer: 5×3×4×2=120 Question 2 A manufacturing operation consists of 10 operations. However, six machining operations must be completed before any of the remaining four assembly operations can begin. Within each set of five, operations can be completed in any order. How many different production sequences are possible? Answer: 6!×4!=17280 Question 3 In the laboratory analysis of samples from a chemical process, five samples from the process are analyzed daily. In addition, a control sample is analyzed two times each day to check the calibration of the laboratory instruments. a) How many different sequences of process and control samples are possible each day? Assume that the five process samples are considered identical and that the two control samples are considered identical. Answer: 7 2 =21 b) How many different sequences of process and control samples are possible if we consider the five process sample to be different and the two control samples to be identical Answer: 2520 5 7 = P , exactly 5! times the previous answer.
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