Question

Question 1.4 (C1) A group of students are each making a single appointment to speak with a Dr. Jekyll one a) If there are 14 students, explain why we cannot guarantee that at least 4 of them meet with Dr. J. on b) Even though[2.8-3, explain why we cannot guarantee that at least 3 of them meet with Dr. c) If we guarantee that no matter how they make their appointments, there is a day of the week on which 5 week (only weekdays allowed, M-F). Answer the following questions: the same day. Jekyll on Thursday students are meeting with Dr. J, at least how many students can you deduce are in the group?

Answer 1

a]

There are 14 students in a group

Students are meet to Dr. Jekyll in weekdays Mon, Tues, Wend, Thurs, and Friday there are only 5 days allowed in week

If at least 4 students meets to Dr. Jekyll on the same day of week then there are at least 4*5 = 20. We need at least 20 students in the group but actually we have only 14 students. Hence we cannot guarantee that at least 4 students meets to Dr. Jekyll on the same day.

b]

Even though 14/5 = 2.8 near about 3 students

If at least 3 students meets to Dr. Jekyll on the same day of week then there are at least 3*5 = 15. We need at least 15 students in the group but actually we have only 14 students. Hence we cannot guarantee that at least 4 students meets to Dr. Jekyll on the same day.

c]

If there are 5 students meets to Dr. Jekyll on the same day of week then there are at least 5*5 = 25. We need at least 25 students in the group. Hence we canguarantee that at least 5 students meets to Dr. Jekyll on the same day in weekdays if we have at least 25 students in the group.