Standoffs in the lone-divider method. In the lone-divider method, a standoff occurs when

QUESTION:

Standoffs in the lone-divider method. In the lone-divider method, a standoff occurs when a set of k choosers are bidding for less than k items. The types of standoffs possible depend on the number of players. With N = 3 players, there is only one type of standoffthe two choosers are bidding for the same item. With N = 4 players, there are three possible types of standoffs: two choosers are bidding on the same item, or three choosers are bidding on the same item, or three choosers are bidding on just two items. With N = 5 players, there are six possible types of standoffs, and the number of possible types of standoffs increases rapidly as the number of players increases. (a) List the six possible types of standoffs with N = 5 players. (b) What is the number of possible types of standoffs with N = 6 players? (c) What is the number of possible types of standoffs with N players? Give your answer in terms of N. (Hint: You will need to use the formula for the number of pairwise comparisons among a set of objects.)