In a certain hotel, the lock on the door to each room can be opened by inserting a key card. The key card can be inserted only one way round. The card has a pattern of holes punched in it. The card has 4 columns, and each column can have either 1 hole, 2 holes, 3 holes or 4 holes punched in it. Each column has 8 different positions for the holes. The diagram illustrates one particular key card with 3 holes punched in the first column, 3 in the second, 1 in the third and 2 in the fourth.

(i) Show that the number of different ways in which a column could have exactly 2 holes is 28.

(ii) Find how many different patterns of holes can be punched in a column.

(iii) How many different possible key cards are there?