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Three consecutive traffic signals each show either red or green. How m

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Bunuel
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Three consecutive traffic signals each show either red or green. How m [#permalink] New post   17 Jan 2016, 12:09
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Question Stats:

73% (00:58) correct 27% (01:04) wrong based on 166 sessions
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Three consecutive traffic signals each show either red or green. How many different arrangements of the three signals are possible? (Note: “Red-redgreen” is different from “green-red-red.”)

A. 10
B. 9
C. 8
D. 7
E. 6
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C
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chetan2u
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Re: Three consecutive traffic signals each show either red or green. How m [#permalink] New post   17 Jan 2016, 21:16
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Bunuel wrote:
Three consecutive traffic signals each show either red or green. How many different arrangements of the three signals are possible? (Note: “Red-redgreen” is different from “green-red-red.”)

A. 10
B. 9
C. 8
D. 7
E. 6


Hi,
The best way to do this Q would be to find the ways separately for each type of arrangements..
all three of same colour= 1*2(for green and red)= 2..
two of one colour and third different colour= 3!/2!=3..
total= 1*2+3*2=8
C
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Re: Three consecutive traffic signals each show either red or green. How m [#permalink] New post   19 Jan 2016, 21:06
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Hi All,

Since the answer choices to the question are so small (relatively speaking), you can get to the correct answer without having to do any fancy calculations. With a drawing and a bit of 'brute force', you can answer this question relatively quickly.

We're told that 3 consecutive traffic signals each show either red or green. We're asked how many different arrangements of the three signals are possible.

The options are:
RRR
RRG
RGR
RGG

GGG
GGR
GRG
GRR

Total Options: 8

Final Answer:
Show Spoiler
C


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MathRevolution
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Re: Three consecutive traffic signals each show either red or green. How m [#permalink] New post   20 Jan 2016, 02:23
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Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.

Three consecutive traffic signals each show either red or green. How many different arrangements of the three signals are possible? (Note: “Red-redgreen” is different from “green-red-red.”)

A. 10
B. 9
C. 8
D. 7
E. 6


Each traffic signal has two different possibilities(green and red). So there are 2*2*2= 8 different possibilities.

So the answer is (C).
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abs8
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Re: Three consecutive traffic signals each show either red or green. How m [#permalink] New post   05 Feb 2022, 04:57
Each of the 3 positions has only 2 possibilities ie RED or GREEN.

Therefore, \(2*2*2 = 8\)

Option C
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Aravind04
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Re: Three consecutive traffic signals each show either red or green. How m [#permalink] New post   05 Mar 2022, 12:19
Number of possibilities is 2 i.e Red or Green and this happens 3 times so 2^3 =8
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Re: Three consecutive traffic signals each show either red or green. How m [#permalink]
05 Mar 2022, 12:19
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