I'm having trouble using a Permutation formula for finding out how many different ways there are to seat 264 people at 481 desks. The trouble I'm having is that in the Permutation formula (nPr = n! / (n–r)!) n would be the distinct people (264) and r would be the number of desks (i.e. spots) to fill (481).
But this calculation doesn't work, as 264 – 481 = (-217), for which you cannot calculate the factorial.
So my question is, is it possible to calculate the number of different ways a number of distinct objects can be placed into a greater number of places, as with my example above? Can r be greater than n in the Permutation formula? And if so, how?
Thanks in advance for any help.
Best Answer
I think you can just think of it as how many ways can I rearrange 264 people and 217 "empties" Something like $\frac{481!}{217!}$
481! ways to arrange the seats, but 217! ways the empties could be arranged identically.
Another way would be to think of it like this: Person 1 can be seated in any of 481 seats. Person 2 has 480 choices.
$481*480*479*\dots*(481-263)=\frac{481!}{217!}$