GATE 2021 CS – Question 29

Engineering Mathematics · Discrete Mathematics: Combinatorics (Counting, Recurrence Relations, Generating Functions) · 1 mark · Numerical answer

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 ______.

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Correct answer: 65

Explanation

The toughest and easiest jobs are fixed. The other 4 jobs go to any of 3 computers, but the middle computer needs at least one: 3^4 - 2^4 = 81 - 16 = 65.