consider a bank of 3 switctes.the switch can only be on or off .1 for on ,. 0 for off .?

Question

a) how many combinations of switch positions are possible for the bank of 3 switches (for example for 2 switches , one combination would be 1,1).state the the appropriate counting rule tha you used

b) list each combination of switch positions for the bank of 3 switches ,. what method do you use to get the list

Answer 1

This is the binary system and it is used by computers and CD players. From the left the switches represent the numbers 4, 2, and 1
4 : 2 : 1
0 : 0 : 1 = 1
0 : 1 : 0 = 2
0 : 1 : 1 = 2+1=3
1 : 0 : 0 = 4
1 : 0 : 1 = 4+1=5
1 : 1 : 0 = 4+2=6
1 : 1 : 1 = 4+2+1=7
The next 3 switches would represent the numbers 8,16, and 32. In binary at least 1 switch must be on, therefore 000 is not admissible.

Answer 2

a) the rules used is : n of combinations of n different objects on k places = (n)^k

b) binary counting.

Answer 3

a) 8

000
100
010
110
001
101
011
111