Question

Fifteen freshmen are sitting in a circle around a table, but the course assistant (who remains standing)
has made only six copies of today’s handout. No freshman should get more than one handout, and any
freshman who does not get one should be able to read a neighbor’s. If the freshmen are distinguishable
but the handouts are not, how many ways are there to distribute the six handouts subject to the above
conditions
it came from here http://goodmathsproblems.blogspot.com/

Answer 1

The answer is 125.
The solution is this: you are one the freshmen, so there is a 6/15 chance to get one copy of the handout.The question now is how many ways are there to distribute the rest?
Going around the table, there are 6 gaps between people with people with handouts. The size of the gaps are from 0 to 2, so the sum of their sizes are 11. So we have two possible gap sizes - 1, 1, 1, 2, 2, 2 or 0, 1, 2, 2, 2. We have 6!/ 3!3! = 20 and 6!/1!1!4! = 30, so there are 20+30 possibilities.Multiplying this by 15/6 gives us 125.