Fifteen students are sitting around a large circular table for a study session. The teacher has made only six copies of the review guide. No student should get more than one copy of the review guide and any student who does not get one should be able to read a neighbor’s copy. If the students are distinguishable, but the review guides are identical, how many ways are there to distribute the six review guides to the fifteen students subject to these conditions?
First I would find ways to arrange the fifteen students so
$(15-1)! = 14!$
Then to arrange the $6$ copies of the review guide, I would use combination so
$15~C~6 = 5005$
But when I multiply these $2$ numbers, I get a huge number.
Do I even need to arrange the fifteen students, or is the answer just $5005$ or is it wrong altogether?