A rotary switch may take one of six positions in response to

A rotary switch may take one of six positions in response to voltage inputs. As a system safety designer you have the option of designing the system so that the switch must take two random settings during a mission or only one. However, if you must design for two settings only one position of the switch will be unsafe. If you design for one setting, two positions will be unsafe. Which is the preferred design?

Solution

If we design for 2 settings: 1 position can be unsafe in: 6C1 = 6 ways and there are 2 settings, so total number of unsafe options: 6*2 = 12

If we design for 1 setting: 2 positions can be unsafe in: 6C2 = 15 ways and there is 1 setting, so total number of unsafe options: 15*1 = 15

Since total number of unsafe options is lower in 2 settings design - hence the 2 settings design is the preferred option.