A special type of door lock has a panel with five buttons labeled with the digits 1 through 5. This lock is opened by a sequence of three actions. Each action consists of either pressing one of the buttons or pressing a pair of them simultaneously. For example, 12-4-3 is a possible sequence. The sequence 12-4-3 is the same as 21-4-3 because the 12 or the 21 simply means to press buttons 1 and 2 simultaneously.
(a) How many different sequences are possible?
(b) How many different sequences are possible if no digit (or pair of digits) is repeated in the sequence?