"A certain music school has 49 students, with 10 each studying violin, viola, cello, and string bass. The director of the school wishes to divide the class into 10 string quartets; the four students in each quarter study the four different instruments. In how many ways can this be done?"
This is question from my discrete math textbook. It's under partitions and equivalence classes. I have no idea how to start this problem. Any hints?
I can't seem to justify my answers enough to convince myself. I think the answer that makes most sense to me is:
40! / (10!4!)
Because there are 40 possible students (no repetition allowed), and they are partitioned into 10 groups of 4-unique elements.
Best Answer
Line up the violinists say in alphabetical order.
Now pick a violist, a cellist, and a bass for the first violinist ($10^3$ ways).
Now pick a violist, a cellist, and a bass for the second violinist ($9^3$ ways).
And so on.
Do you see what happens from here?