Organizing 12 Programs: Priority, No Restrictions & More

[ashkash]

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.

 

[durt]

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).

 

[ashkash]

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?

 

[durt]

Perhaps you should read http://en.wikipedia.org/wiki/Rule_of_product" , 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.

 

[ashkash]

got it, thanks.