Can anyone give me some guidance here?


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?

 Mar 13, 2020

a) On each action, there are 15 possible inputs: 5 inputs consisting of a single button, and 10 inputs consisting of two different buttons.

 Mar 13, 2020

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