I have a problem that goes like this:
7 people are at a restaurant. The restaurant has a menu which has four unique items from which the 7 men choose from. Each men orders one of the 4 meal options and gives their choice to the waiter. However, the waiter accidentally loses the paper that tells him what each person ordered. The waiter then tells the cook to just make whatever he wants and hope for the best (make 7 meals randomly choosing one of the 4 options for each person). What are the chances (probability) that each man actually receives what he ordered (basically that the group 7 items that were randomly made can be given such that each man can receive what he wanted)?
I saw a youtube video of someone trying to explain this problem and I wasn't quite convinced that the answer was (1/120) even though there are 120 different combinations the cook can make.
This is the video: His original problem is here, starting at 1:00 :youtube.com/watch?v=ILAGckNjXvo. And his solution is here at 2:15 : youtube.com/watch?v=E31aGpE8TH0.
What is the best way to approach this problem? Are the 120 combinations actually equally likely to be made by the cook?