Martha, Lee, Nancy, Paul, and Armando have all been invited to a dinner party. They arrive randomly and each person arrives at a different time In how many ways can they arrive?

To solve this problem you have to use permutations. Permutations are where you have a group of things and you want to see how many different combinations you can make, but for these combinations the ordering matters. This would be 5P5 and the answer is they can arrive in 120 different ways.