Gary has 7 suits. in how many different ways can he arrange the suits in his wardrobe?

If Gary has seven suits, he can choose which of the seven he will place first. He can choose from the remaining six which one he will place next. This goes on until all the suits are placed in his wardrobe. In short, he can arrange his suits in 7! (7 factorial) ways in his wardrobe. 
 
                                  7! = 5040

Thus, Gary can arrange his suits in 5040 ways.