Question

Chamberlain, Kelly MATI27: Te NAME: 3. Choosing on-off settings. Determine the number of possible settings for a row of five on-off switches under each condition a) No restrictions stat b) The first, third, and fifth switches must be on (5 pts) c) No two adjacent switches can be both on (You must show a tree diagram 5pts and count the solutions 5 pts)

Answer 1

c) No two adjacent switches must be ON

Question 3: a) No restrictions 2 2 2 2 N Each of the switches has two possibilities i.e. ON OR OFF. The total number of possible settings hence is given as = 2*2*2*2*2 = 32 b) First, third and fifth switch must be ON ON 2. ON 2 ON Switch number 2 and 4 have two possibilities i.e. ON OR OFF. Switch number 1, 3 and 5 are fixed The total number of possible settings hence is given as = 2*2 = 4

From the above tree diagram, the total number of possible settings is 8.

Switch-ah tswitch-s ON switch -5 z ON Switch- OFF OFF (Switch-4 3 OFF - Switch-5 Iswitch-2 4 ON swithh-5 ON a off Switch-1 twitch-4 5 switch-3 Switch- OFF ON OFF 6 Switch-2 Switchs (with-a ON OFF switch-3 twitch 5 ON OFF Switch-4 OFF Switch- 58