Matthew finds that 12 computer programs have been submitted for batch processing. In how many ways can he order the processing of these programs if:
(a) he considers four of the programs higher in priority than the other eight and wants to process those four first?
(b)he first seperates the programs into four of top prority, five of lesser priority, and three of least priority, and he wishes to process the 12 programs in such a way that the
top-priority programs are processed first and the three programs of least priority are processed last?

Question

Matthew finds that 12 computer programs have been submitted for batch processing. In how many ways can he order the processing of these programs if:
(a) he considers four of the programs higher in priority than the other eight and wants to process those four first?
(b)he first seperates the programs into four of top prority, five of lesser priority, and three of least priority, and he wishes to process the 12 programs in such a way that the
top-priority programs are processed first and the three programs of least priority are processed last?

anonymous · Answer

(a) 
Important Info:
12 CPU programs
order matters: selecting 4 programs out of the 8 
and then processing them first
counting principal used: permutation

r = 4
n = 8
P(n,r) = P(8,4) = 1680 ways 

^ I'm not 100% sure if n should be 8 or 12

anonymous · Answer

(b) 
Important Info:
order matters: 4(top priority), 5(lesser priority), 3(least priority)

Since the question has "and" in it and can be 
broken down into multiple stages (priorities),
using the "rule of product" I get:
P(8,4) * P(7,5) * P(9,3) = 1680*2520*504=2133734400 ways
^I'm also not sure about the n here