**Question:-**

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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