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Unformatted text preview: ATIONS Solution: There are three orderings: AAB, ABA, BAA. But if we put labels on the two A’s,
writing them as A1 and A2 , then the three letters become distinct, and so there are 3!, equal to
six, possible orderings:
A1 A2 B A 2 A1 B
A1 BA2 A2 BA1
BA1 A2 BA2 A1 .
These six orderings are written in pairs that would be identical to each other if the labels on the A’s
were erased. For example, A1 A2 B and A2 A1 B would both become AAB if the labels were erased.
For each ordering without labels, such as AAB, there are two orderings with labels, because there
are two ways to order the labels on the A’s. Example 1.3.4 How many orderings of the letters ILLINI are there, if we don’t distinguish the
I ’s from each other and we don’t distinguish the L’s from each other?4
Solution: Since there are six letters, if the I ’s were labeled as I1 , I2 , I3 and the L’s were labeled
as L1 and L2 , then the six letters would be distinct and there would be 6!=720 orderings, including
I1 I3 L2 N I2 L1 . Each ordering wit...
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This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Institute of Technology.
- Spring '08
- The Land