# Clever Counting by 6Zm93B8d

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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
 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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