A university schedules its final examinations in 18 examination group" so that courses held at different times are in different examination groups. The examination times are spread over 6 days, with 3 examinations each day. Suppose all students take 4 examinations. About what proportion of students will have their 4 examinations on different days? [You need to make some assumptions-state what the assumptions are]
The matching problem. There are n letters addressed to n people at n different addresses. The n addresses are typed on n envelopes. A disgruntled secretary shuffles the letters and puts them in the envelopes in random order, one letter per envelope.
a) Find the probability that at least one letter is put in a correctly addressed envelope. [Hint: use the inclusion-exclusion formula of Exercise 1.3.1.2]
b) What is this probability approximately, for large n?