This problem actually relates to multi processing computer architecture, but boils down to a mathematical expression quite difficult to understand.
The image below explains the problem and the last expression (N-1)C(r-1) is some thing I am NOT able to understand.
I took an example of 9 tasks and 3 levels so that N=9 and r=3. Going by the description at the bottom, each level at least should have one task and hence division of rest of 6 tasks in three levels counts the number of process graphs. I did try as below :
Enumerate in how many ways number 6 be partitioned in three places :
2,2,2 <-- Only 1 way to express so that it totals to 6
1,1,4 <-- Only 3 ways to express so that it totals to 6
3,2,1 <-- 6 ways to express so that it totals to 6
4,2,0 <-- 6 ways to express so that it totals to 6
5,1,0 <-- 6 ways to express so that it totals to 6
6,0,0 <-- Only 3 ways to express so that it totals to 6
3,3,0 <-- Only 3 ways to express so that it totals to 6
So in all this totals to 1+3+6+6+6+3+3 = 28 ways
Going by the expression the value should be 8C2 which evaluates to 28.
However, what I lack is to understand, how we have arrived at the result (N-1)C(r-1).
Thanks for reading.