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5. A search committee is formed to find a new software engineer. (a) If 100 applicants apply for the job, how many ways are there to select a subset of 9 for a short list? (b) If 6 of the 9 are selected for an interview, how many ways are there to pick the set of people who are interviewed? (You can assume that the short list is already decided) (c) Based on the interview, the committee will rank the top three candidates and submit the list to their boss who will make the final decision. (You can assume that the interviewees are already decided.) How many ways are there to select the list from the 6 interviewees?

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(a) Number of ways to select a subset of 9 for a 100 100 or short list from 100 applicats 9 (there is no ordering in the subs

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