Problem Solving

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

oa IS 2

sana.noor wrote: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

oa IS 2

Total number of pairs that can be formed from the 25 students = 25C2 = (25*24)/(2*1) = 300.
Over the course of the term, each of these pairs must appear exactly ONCE.

Each day 4 students are selected.
The number of pairs that can be formed from the 4 students selected each day = 4C2 = (4*3)/(2*1) = 6.
Thus, each day accounts for 6 of the 300 pairs that must appear over the course of the term.

Since there are 300 possible pairs, and 6 of these pairs will appear each day, the total number of days needed = 300/6 = 50.

The correct answer is D.