what are the possible permutations of 7 switches that can be either on or off
Answers
Answer:
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Step-by-step explanation:
say you had 2 switches
each one is either on (O) or off (F)
2*2=4
OO
OF
FO
FF
say you had 3 switches
2*2*2=8
FFF
OFF
FFO
FOF
OOO
OOF
FOO
OFO
if you had 7 switches...
2*2*2*2*2*2*2=128
Answer:
This case is binary. For a binary case all the possible permutations can be calculated by the following formula
p=2n
where p is the number permutations and n the number of switches. The formula comes from the following argument.
Consider one switch, the possible permutations are either 1 or 0. For two switches, first fix a value for the first switch (lets fix it on 0), so the possible permutations are (0,0) and (1,0). Now, fix the first switch with the value 1, then the possible permutations are (0,1) and (1,1), the number of permutations is double. Each time you add a switch the former permutations doubles. So, if you have two switches the permutations are 2x2, for three switches the former number of permutations is doubled, then for three switches the permutations are (2x2)x2 , and so on. The following table could be useful to improve the understanding
One switch
2=21
two switches
2x2=22
three switches
2x2x2=23
four switches
2x2x2x2=24
n switches
2x2x2...x2=2n
For this case, if you want to write all the possible permutations, you can do it as follows
0000
0001
0010
0011
0100
0101
0110
0111
1000
1001
1010
1011
1100
1101
1110
1111
Note that digits that are on the right, switch from 0 to 1 every row, the second digit from right to left switches from 0 to 1 every two rows, the third digits from right to left switches from 0 to 1 every four rows and the digit on left switches from 0 to 1 every eight rows.
Step-by-step explanation:
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