The following problem is from my probability and statistics book:
A fraternity consisting of 30 members wants to play "seven versus seven" flag football. How many different match-ups are possible?
This question is asked after the partitioning/multinomial coefficients section so I know there must be a solution using this method. I thought it was simple:
30! / (7! * 7! * 16!) = 4.9909.. * 10^11
30C7 * 23C7 = 4.9909.. * 10^11
however the solution in the back of the book is 2.495*10^11
I cannot figure out how they got this answer. Does anybody else have any ideas?
Thank you for your time!