The Formula

Now, we can begin to derive the formula to determine the number of permutations for a given number of objects, and a given number of spaces. For our example, there were 3 objects and three spaces. This is not always the case. Let's say there were only 2 tickets, or there were 4 tickets, so four places in line they could have occupied. Obviously, this changes the number of possible permutations.
To compute the number of permutations for n objects, with k places to put them in, we can use the following formula:

P(n,k) = n·(n-1) ···(n-k+1) = n!/(n-k)!
So, to compute for our example with 3 people and 3 places in line, we could perform the calculations:
P(3,3) = 3!/(3-3)! = (3*2*1)/(1) = 6

SCLM Completed for CS 561 Spring 2004. Questions? Comments? Email Charles Bauer.