Organizing 12 Programs: Priority, No Restrictions & More

  • Thread starter ashkash
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In summary: So it would be 4!*8! for part b?In summary, for a. you can order the 12 programs in 12! ways with no restrictions. For b. you can order the first group of 4 in 4! ways and the next group of 8 in 8! ways, for a total of 4!*8! ways. For c. you can order the top priority group of 4 in 4! ways, the lesser priority group of 5 in 5! ways, and the least priority group of 3 in 3! ways, for a total of 4!*5!*3! ways.
  • #1
ashkash
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The question is as follows:

You have 12 programs that need to be processed. How many ways can you order these 12 programs if

a. there are no restrictions?
b. you consider 4 programs higher in priority than the other 8 and want to process those 4 first?
c. you separate the programs into 4 of top priority, 5 of lesser priority, and 3 of least priority and you want to process them so the top priority is processed first and the 3 programs of least priority are processed last?

So far this is what I have:
a. 12!
b. 12!/4!
c. 12!/(4!5!3!)

Can anyone please help in and let me know if this looks right or if I am doing anything wrong. thanks.
 
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  • #2
Could you show your work for b. and c.? Consider how many ways you can order the first group (of 4), then consider how many ways you can order the second group (of 8).
 
  • #3
for b:

you can order the first group of 4 in 4! ways and the next group of 8 in 8! ways. So would it be 12!/(4!8!) for part b?
 
  • #4
Perhaps you should read http://en.wikipedia.org/wiki/Rule_of_product" [Broken], and take special notice to the line: "Stated simply, it is the idea that if we have a ways of doing something and b ways of doing another thing, then there are a · b ways of performing both actions."

I'm not sure why you have that 12! in there.
 
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  • #5
got it, thanks.
 

1. What is the best way to prioritize 12 programs?

The best way to prioritize 12 programs is to first determine the goals and objectives of each program. Then, rank them according to their importance in achieving those goals. Consider factors such as impact, urgency, and resources required.

2. How do I organize 12 programs with no restrictions?

When organizing 12 programs with no restrictions, it is important to first define the scope and objectives of each program. Then, consider the resources and timeline available to determine the best way to structure and schedule the programs. Collaboration and clear communication between all stakeholders is key in this process.

3. What are some common challenges when organizing 12 programs simultaneously?

Some common challenges when organizing 12 programs simultaneously include conflicting priorities, limited resources, and communication gaps. It is important to have a clear understanding of the goals and objectives of each program, as well as open communication and flexibility to address any challenges that may arise.

4. How can I ensure that all 12 programs are running efficiently?

To ensure that all 12 programs are running efficiently, it is important to regularly review and evaluate their progress. This can include tracking key performance indicators, identifying any bottlenecks or areas for improvement, and making necessary adjustments to optimize efficiency.

5. Is it possible to have a contingency plan for all 12 programs?

Yes, it is possible to have a contingency plan for all 12 programs. This involves identifying potential risks and developing strategies to mitigate or address them. It is important to regularly review and update the contingency plan to ensure preparedness for any unforeseen circumstances.

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