GATE CSE 2021 Set 1 Q29: Assigning 6 ranked jobs to 3 ranked computers
- Engineering Mathematics
- 1 mark
- NAT
- No negative marking
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 ________.
Try it: numerical answer: type the value
Show answer and explanation
Answer: 65 (official GATE 2021 final answer key)
Concept used: Fix the two forced assignments, then count functions from the remaining jobs with one at-least-one condition.
First step: The other 4 jobs go to any of 3 computers, but the middle computer must receive at least one: minus the assignments that avoid it.
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Source: official GATE 2021 Set 1 CS question paper and final answer key, organised by IIT Bombay. Question paper · Answer key
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