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. 65

Answer 1

The correct option is A 65
Let computers be A, B and C
Toughest job assigned to fastest computer (Say, A) is 1 way.
Easiest job assigned to shortest computer (Say, B) is 1 way.
Remaining 4 jobs to be assigned to 3 computers so that the computer C gets at least one job, since A and B already assigned a job. Number of ways 4 jobs assigned to 3 computers = $3^4$.
Number of ways 4 jobs assigned to 3 computers, so that computer C does not get any job = $2^4$. Required number of ways = $3^4$ - $2^4$ = 81 - 16 = 65 ways