There are 6 jobs with distinct difficulty levels, and 3 computers with distinct processing speeds. Each job is assigned ...

Question

There are 6 jobs with distinct difficulty levels, and 3 computers with distinct processing speeds. Each job is assigned to a computer such that:
- The fastest computer gets the toughest job and the slowest computer gets the easiest job.
- Every computer gets at least one job.
The number of ways in which this can be done is ______.
A. 3
B. 5
C. 65
D. 15

Accepted Answer

65 Label computers C1 (slowest), C2 (medium), C3 (fastest) and jobs J1 (easiest) through J6 (hardest). Two assignments are forced: J1 to C1 and J6 to C3. The 4 remaining jobs (J2, J3, J4, J5) must be assigned to the 3 computers so that C2 gets at least one job (C1 and C3 already each have one). The count is (all assignments of 4 jobs to 3 computers) minus (assignments where C2 gets nothing).