Suppose in Self-Test Problem 1 that the 20 people are to be seated at seven tables, three of which have 4 seats and four of which have 2 seats. If the people are randomly seated, find the expected value of the number of married couples that are seated at the same table.
Problem 1
Twenty individuals consisting of 10 married couples are to be seated at 5 different tables, with 4 people at each table.
(a) If the seating is done “at random,” what is the expected number of married couples that are seated at the same table?
(b) If 2 men and 2 women are randomly chosen to be seated at each table, what is the expected number of married couples that are seated at the same table?
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