Data Management: Premutations Problem With identical Items

In summary, there are 4032 possible ways for the positions of secretary, treasurer, social convenor, and fundraising chair to be filled if the Norman twins are running and plan to switch positions on occasion for fun. This is calculated by breaking the problem into three cases and treating the twins as indistinguishable. The book answer of 5040 may be incorrect.
  • #1
gurjant
1
0

Homework Statement


Ten students have been nominated for positions of secretary, treasurer, social convenor, and fundraising chair. In how many ways can these positions be filled if the Norman twins are running and plan to switch positions on occasion for fun since no one can tell them apart?

txt book answer:4032

Homework Equations


n! factorials

nPr= n!/(n-r)! premutations

n!/(a!b!c!...) premutations with identical items


The Attempt at a Solution


10P4=5040 totals ways nominations can be picked

i don't know how to find the number of ways twins can be picked/ answer
 
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  • #2
I guess we are to treat the twins as indistinguishable. So try breaking the problem up into three cases:
(1) No twin holds a position;
(2) Exactly one twin holds a position;
(3) Both twins hold positions.

I think I should warn you that I don't get the book answer. So I'm going to stick my neck out and say that the book is wrong. Of course, it may be that I have misinterpreted the problem. I do that a lot.
 

1. What is the Premutations Problem with identical items?

The Premutations Problem with identical items refers to a scenario where you have a set of items that are identical, meaning they have the same value or characteristics. In data management, this can pose a challenge because it can be difficult to differentiate or group these items together.

2. How does the Premutations Problem affect data management?

The Premutations Problem can affect data management in a few ways. It can make it difficult to accurately count or track these identical items, as well as make it challenging to identify and organize them in a meaningful way. This can lead to errors or inconsistencies in data analysis.

3. What are some strategies for managing the Premutations Problem?

One strategy for managing the Premutations Problem is to assign a unique identifier to each identical item. This could be a serial number, barcode, or any other unique identifier that can differentiate between the items. Another strategy is to use data cleaning techniques to identify and remove any duplicate entries.

4. How can data management systems handle the Premutations Problem?

Data management systems can handle the Premutations Problem by implementing features such as duplicate detection and removal, as well as allowing for the use of unique identifiers for identical items. They can also have built-in algorithms that can handle permutations and group identical items together.

5. What are the implications of not properly managing the Premutations Problem?

If the Premutations Problem is not properly managed, it can lead to inaccurate data analysis and decision-making. It can also result in data duplication, which can take up storage space and make data management more challenging in the long run. Additionally, it can affect the overall data quality and reliability.

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