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?
- A66
- B55Correct
- C54
- D45
Explanation
To find the total number of comparisons between 11 people where each person is compared with every other person, we use the formula for combinations of 11 items taken 2 at a time. This is because a comparison involves a pair of individuals, and the order of the individuals in that pair does not matter.
The mathematical formula is n multiplied by n minus 1, all divided by 2. Here, n is 11.
So, the calculation is 11 multiplied by 10, which equals 110. Then, 110 divided by 2 equals 55.
Therefore, 55 comparisons are needed in total. The correct option is B.
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