1. ## partitioning/multinomial coefficients

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
or:
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?

2. Originally Posted by probstud
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
or:
30C7 * 23C7 = 4.9909.. * 10^11

however the solution in the back of the book is 2.495*10^11
$\dfrac{\mathcal{C}(30,7)\cdot\mathca{C}(23,7)}{2}= 249545310300$.
Divide by two to account for symmetry.