By Nosika Qirjaku
A permutation is the rearrangement of distinct elements in an ordered list L into a one-to-one correspondence with L itself.
The number of ways of obtaining an ordered subset of n elements from a set of r elements is given by:
P(n,r) = n!/ (n-r)!
where n and r are natural numbers and n > 1, 0 < r < n, and where P(n,r) is initialized by P(n,0)=1, which is also called the empty permutation.
Real-World Example
You are the group leader for a project in Math class. Your teacher asks you to work with 4 other students. He/She wants a list of the members of your group (including you). In how many ways can you list all 5 names?
Solution: You could just say that since there are 5 people you'll have 5! = 120 ways to choose, or you could use the formula P(5,5) = 5!/0! = 120 ways.