The pushbutton combination lock has a lock bolt mechanism with a lock bolt movably mounted on a frame between a locking position and an unlocking position. The lock bolt mechanism further has two lock bolt actuating mechanisms arranged to move the lock bolt between the locking position and the unlocking position. The lock has a pushbutton combination locking mechanism for locking the first lock bolt actuating mechanism to prevent the lock bolt from being moved by the first lock bolt actuating mechanism to the unlocking position while the second lock bolt actuating mechanism is independent from the pushbutton combination locking mechanism. The pushbutton combination locking mechanism is further rotatably or slidably mounted to the frame such that the user can choose the side for locking and the side for free operation.