Hi,I have another question, how many channels are needed for six different tv st
ID: 3012284 • Letter: H
Question
Hi,I have another question,
how many channels are needed for six different tv stations whose distance from one another is shown below
A
B
C
D
E
F
A
0
85
175
100
50
100
B
85
0
125
175
100
130
C
175
125
0
100
200
250
D
100
175
100
0
210
220
E
50
100
200
210
0
100
F
100
130
250
220
100
0
Assume that two stations cannot use the same channel if they are within 150 miles of one another.
SO Here's my what I think A and C are seperated by 175 miles,so they can share the same channel,so A will require 5 channels out of which one will be shared by C
similarly B is seperated from C and D by 125 and 175respectively so again it will rquire 5 channels out of which c and D will be sharing channels with B
Now C is seperated from E and F by 200 and 250 respectively,so its channel will be shared by E and F and it already shares a channel with A and B,so for C no of channels are 3
for D by the same reasoning no of channels are 2 for A and B
and for E the number of channels are 3
and for F it is 3
hence the total no of channels are 5.5.3.2.3.3 or should it be 5+5+3+2+3+3
A
B
C
D
E
F
A
0
85
175
100
50
100
B
85
0
125
175
100
130
C
175
125
0
100
200
250
D
100
175
100
0
210
220
E
50
100
200
210
0
100
F
100
130
250
220
100
0
Explanation / Answer
Here all possible channels of all 6 stations will be added together it is because this is the case of either or as events are mutually exclusive here. Thus total channels will be 5+5 +3+2+3+3 = 21
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