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Clever Counting Investigation 5: Wrapping Things Up Catching a Bicycle Thief Problem 5.1 You now know as much as the detective does about counting combinations and calculating probabilities. Which pieces of evidence would you investigate further? How would you proceed with your investigation? What questions would you ask the security guard, the manager, or someone else involved in the case? Does the evidence from the second robbery clear any of the suspects? Who are your suspects now? Why? Problem 5.1 Follow-up #1 A. One of the smudged serial numbers was UM_ _ _ 7711. The first blank represents a letter, the other two are numbers. In how many ways can this serial number be completed? B. The bike at the manager’s home had the serial number UMZ567711. Based on your findings from A, can you draw any conclusions about the manager’s guilt or innocence? Explain. Problem 5.1 Follow-up #2 A. Assume that all mountain bikes have serial numbers with three letters followed by six numbers. How many possible combinations are there for the first two letters and the last four numbers of the serial number for a mountain bike? B. What are the chances that the serial number on the manager’s bike would contain the sequence UM _ _ _ 7711? C. Based on your findings, can you draw any conclusions about the manager’s guilt or innocence? Explain.
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