Each person`s performance compared with all other persons is to be done to rank them subjectively. How many comparisons are needed in total, if there are 11 persons?

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Submitted by examrobotsa on

Q: 117 (IAS/2010)
Each person's performance compared with all other persons is to be done to rank them subjectively. How many comparisons are needed in total, if there are 11 persons?

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,8,1,1,8,0,0

keywords: 

{'many comparisons': [0, 0, 1, 0], 'performance': [0, 0, 4, 2], 'other persons': [0, 0, 1, 0], 'persons': [4, 4, 9, 10], 'total': [0, 1, 1, 1]}

If we compare each person with all the others, we will have to make (n - 1) comparisons for each person, where n is the number of persons. So, for 11 persons, the number of comparisons needed will be (11-1) times 11, which is equal to 110. However, since each comparison is made twice (e.g. A compared with B and B compared with A), we need to divide 110 by 2, giving us a total of 55 comparisons. Therefore, the correct answer is option B, 55.