This is a true story! Alice was coming up to her final exams, which were set across 18 days. Each of the 18 days had 2 sessions, a morning and an afternoon session. Alice had to complete 6 exams altogether.
When the exam timetable was released, Alice cried, "I'm screwed! I've got two doublers! What are the chances of that?" By this Alice meant that she was disappointed that she had 2 days on which she had to complete 2 exams, one in the morning and one in the afternoon, on that same day. What is the probability that Alice would find her 6 exams set on just 4 days?