mohammadmh91 wrote:
please let me know if i am right.
Each student is given a number, so:
Maryland University students: 1,2,3,4
Ways 3 persons possibly can be selected: (1,2,3) ,(1,2,4), (1,3,4),(2,3,4)
Vermont University students: 5,6,7,8
Ways 3 persons possibly can be selected: (5,6,7) ,(5,6,8), (5,7,8),(6,7,8)
Emory University students: 9,10,11,12
Ways 3 persons possibly can be selected: (9,10,11) ,(9,10,12), (9,11,12),(10,11,12)
Number of ways a team of 9 is formed:
(1,2,3)(5,6,7)(9,10,11)
(1,2,3)(5,6,7)(9,10,12)
(1,2,3)(5,6,7)(9,11,12)
(1,2,3)(5,6,7)(10,11,12).....
so there are 64 different teams of 9 persons selected equally from 3 Universities
The question is not asking for the number of different teams that can be formed, in which case you are right. The question is asking how many number of ways the selections can be done.
We can select 3 out of 4 players from The University of Maryland in 4!/(3! * (4 - 3)!) = 4 ways
We can select 3 out of 4 players from The University of Vermont in 4!/(3! * (4 - 3)!) = 4 ways
We can select 3 out of 4 players from Emory University in 4!/(3! * (4 - 3)!) = 4 ways
Therefore, the total number of ways the selection can be made is 4 + 4 + 4 = 12 ways