# Thread: partitioning/multinomial coefficients

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?

Thank you for your time!

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
$\displaystyle \dfrac{\mathcal{C}(30,7)\cdot\mathca{C}(23,7)}{2}= 249545310300$.
Divide by two to account for symmetry.