What is the probability in a hat trick 5 people wont get back their own hats?

In hockey when somebody gets 3 goals in one game its customary to throw hats on the ice. I need to find out if there are only 5 spectators at the ring and they throw their hats on the ice, what is the probability the ref will give back the hats and nobody will get their hat? I an having trouble because i have an attached article called Avoiding Your Spouse at a Party Leads to War, it uses what i believe are binomial coefficients and summations. I assume the same are required for my problem. The reason i am having trouble is because I never learned these things. please explain or tell me how to do this.