posted by Cynthia on .
There are 12 students in a class. Find the number of ways that 12 studenets can take 3 different tests if 4 students are to take each test.
Find the number of ways 12 students can be partitioned into 3 teams A, B, C, so that each team contain 4 students.
I don't get what is the difference between the two. For the first one, the book uses C(12,4) * C(8,4) = 34650. I use the permutation method, which is bascially the same 12!/(4!4!4!) = 34650
For the second question, the books tells me to think that A is in team A and you have to chose three different people to join team A, resulting into C(12,3). The same logic applies to team B: C(7,3) and that left 4 for team C.
Therefore the answer was C(12,3) * C(7,3) = 5925.
THe book tells me if you use the partition method, all you do is 34650/6 = 5925 because 3! is an ordered partition. (what is an ordered partition anyway?)