Question

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

Answer 1

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