On the play date for all middle school students, their teacher has decided to take them to Zenith an arcade game arena near the school. The arena has exactly one unit of each type of arcade game like pin ball, car racing, shooting etc. and all these games are single player games, that mean only one player can play the game at a time. In order to keep the students happy and avoid any conflict or fights, the teacher shared a list of arcade games with the students and asked them to pick their favourites. After receiving the forms from each student, the teacher now wants to know how many combinations can she come up with such that: 1. Every student is playing a game of their liking 2. No student is left without a game of their choice 3. No two students are found fighting for the same game. Assuming that all games take the exact amount of time to complete before students have to switch to another game, if there are 10 games and 10 students, find out the number of combinations the teacher has to shuffle students between each of the games. Games: G1, G2, G3, G4, G5, G6, G7, G8, G9, G10 Students: S1, S2, S3, S4, S5, S6, S7, S8, S9, S10