91Ó°ÊÓ

In how many ways can 8 people be seated in a row if (a) there are no restrictions on the seating arrangement? (b) persons \(A\) and \(B\) must sit next to each other? (c) there are 4 men and 4 women and no 2 men or 2 women can sit next to each other? (d) there are 5 men and they must sit next to each other? (e) there are 4 married couples and each couple must sit together?

The game of bridge is played by 4 players, cach of whom is dealt 13 cards. How many bridge deals are possible?

If 8 identical blackboards are to be divided among 4 schools, how many divisions are possible? How many if each school must receive at least 1 blackboard?

We have 20 thousand dollars that must be invested among 4 possible opportunities. Each investment must be integral in units of 1 thousand dollars, and there are minimal investments that need to be made if one is to invest in these opportunities. The minimal investments are \(2,2,3,\) and 4 thousand dollars. How many different investment strategies are available if (a) an investment must be made in cach opportunity? (b) investments must be made in at least 3 of the 4 opportunities?