Policy makers and economists alike have considerable interest in
alternatives to the traditional system of allocating students to
public schools based on their place of residence within a city. One
alternative is a “mechanism design” approach whereby a central
authority assigns students to schools based on some alternative
criterion, such as a list of stated preferences or results of an
aptitude test. Suppose the fictional city of Learnlandia has 20 new
students and seeks to allocate them across four high schools. Each
school has a different specialty: Arts (A), Science (S), History (H)
and Language (L). The four schools have 1, 6, 9 and 4 openings for
new students, respectively.
a) In how many distinct ways can the 20 students be allocated
across the four schools
a) number of ways to divide 20 students so that (1,6,9,4) student in each school with different specialty
=(20!/(1!*6!*9!*4!)) =387987600
Policy makers and economists alike have considerable interest in alternatives to the traditional system of allocating...