SOLUTION: THE ARE 20 STUDENTS AND THEY NEED TO BE ALLOCATED INTO 3 CLASSROOMS.IN HOW MANY WAYS CAN THIS BE DONE 1.ASSUMING THAT THE STUDENTS ARE IDENTICAL 2.ASSUMING THAT THE STUDENTS ARE

Algebra ->  Permutations -> SOLUTION: THE ARE 20 STUDENTS AND THEY NEED TO BE ALLOCATED INTO 3 CLASSROOMS.IN HOW MANY WAYS CAN THIS BE DONE 1.ASSUMING THAT THE STUDENTS ARE IDENTICAL 2.ASSUMING THAT THE STUDENTS ARE       Log On


   

Question 10458: THE ARE 20 STUDENTS AND THEY NEED TO BE ALLOCATED INTO 3 CLASSROOMS.IN HOW MANY WAYS CAN THIS BE DONE
1.ASSUMING THAT THE STUDENTS ARE IDENTICAL
2.ASSUMING THAT THE STUDENTS ARE DISTINGUISHABLE
Answer by khwang(438) About Me  (Show Source):
You can put this solution on YOUR website!
1.ASSUMING THAT THE STUDENTS ARE IDENTICAL
2.ASSUMING THAT THE STUDENTS ARE DISTINGUISHABLE
1. Like the possible solutions of the integral equations
x + y + z = 20 (z,y & z as three classrooms)
Arrange r = 20 possble combinations among n=3 elements.
There are H(n, r) = C(n+r-1, r) = C(22,20) = C(22,2)
=22*21/2 = 21*11 = 231
2. Each student has 3 choices, totally, there 3^20 ways.

Kenny