In a class in a certain school, there are 25 students. Four students are appointed monitors every day. At the end of a term, it is found that every possible pair of students have been monitors together exactly once. How many days are there in the term?
OPTIONS
1) 30
2) 50
3) 60
4) 75
5) None of these
Solution
Every possible pair of students have been monitors together exactly once.
∴ Number of days in the term = ( Total number of unique pairs possible in the class)/(Number of pairs formed per day)
Since a unique pair will be formed when 2 students are selected as monitors on a given day, the total number of unique pairs possible in the class is the same as the total number of ways in which 2 students can be selected from 25 students.
Total number of ways of selecting 2 students from 25 students will be -
Every day, 4 students are selected as monitors.
Therefore, number of pairs formed per day will be =
∴ Number of days in the term = 300/6 = 50
Hence, option 2.
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