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# A traffic signal has 4 colors: Red, Blue, Green, and Yellow. Signals

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Joined: 04 Jan 2015
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A traffic signal has 4 colors: Red, Blue, Green, and Yellow. Signals  [#permalink]

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Updated on: 13 Aug 2018, 07:45
1
3
00:00

Difficulty:

15% (low)

Question Stats:

70% (00:53) correct 30% (00:57) wrong based on 170 sessions

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Learn when to “Add” and “Multiply” in Permutation & Combination questions- Exercise Question #2

A traffic signal has 4 colors: Red, Blue, Green, and Yellow. Signals are made by combining any $$2$$ of these $$4$$ colors. How many unique signals can the traffic signal show if the order of the colors defines unique cases?

A) 3
B) 6
C) 8
D) 12
E) 24

Learn to use the Keyword Approach in Solving PnC question from the following article:

Learn when to “Add” and “Multiply” in Permutation & Combination questions

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Originally posted by EgmatQuantExpert on 04 Apr 2018, 06:38.
Last edited by EgmatQuantExpert on 13 Aug 2018, 07:45, edited 7 times in total.
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Re: A traffic signal has 4 colors: Red, Blue, Green, and Yellow. Signals  [#permalink]

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04 Apr 2018, 07:26
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Signals can be generated by selecting 2 colours and rearranging them.
out of 4 colors: Red, Blue, Green, and Yellow, 2 can be selected in 4C2 ways = 6ways
arrangement = 2! = 2 ways.
No of signals = 6*2 = 12 ways.

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Re: A traffic signal has 4 colors: Red, Blue, Green, and Yellow. Signals  [#permalink]

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04 Apr 2018, 20:33
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EgmatQuantExpert wrote:
Learn when to “Add” and “Multiply” in Permutation & Combination questions- Exercise Question #2

A traffic signal has 4 colors: Red, Blue, Green, and Yellow. Signals are made by combining any $$2$$ of these $$4$$ colors. How many unique signals can the traffic signal show if the order of the colors defines unique cases?

A) 3
B) 6
C) 8
D) 12
E) 24

Permutation
Initially, we choose two colors from four.

The number of ways in which we can "choose" or "select" $$r$$ objects from a group of $$n$$ objects indicates a combination.

BUT order matters: "how many UNIQUE signals" and "the order of colour defines unique."
How the two colors are arranged matters. If order matters, permutation is needed.

The number of arrangements of $$r$$ objects taken $$n$$ at a time = permutation

R, G, B, Y = colors
RG is different from GR

Permutation, $$_{n}P_{r}$$

Formula: $$\frac{n!}{(n-r)!}$$

$$_{4}P_{2}=\frac{4!}{2!}=\frac{4*3*2*1}{2*1}=$$12 unique arrangements

Fundamental Counting Principle:

For the first color, there are 4 choices
No matter which color gets chosen first, after that there are 3 colors from which to select for the second choice

__4___ * __3___ = 12 arrangements

R, G, B, Y:

R chosen first: RG, RB, RY
G chosen first: GR, GB, GY
B chosen first: BR, BG, BY
Y chosen first: YR, YG, YB

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Re: A traffic signal has 4 colors: Red, Blue, Green, and Yellow. Signals  [#permalink]

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08 Apr 2018, 21:30

Solution

Given:
• A traffic light has signals of 4 colours: Red, blue, green and yellow.
• The traffic light will show a signal by combining 2 of these 4 colours.

To find:
• We need to find the number of ways in which 2 colours can be chosen out of 4 colours.

Approach and Working:

Since the picking of 2 different colours gives a different signal, the ways of picking of 2 colours are dependent on each other.
Hence,
• Total ways to pick colours=Number of ways to pick 1 colours from 4 colours and number of ways to pick another colour
• Total ways= 4*3= 12

Hence, the correct answer is option D.

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Re: A traffic signal has 4 colors: Red, Blue, Green, and Yellow. Signals  [#permalink]

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29 May 2019, 09:59
gmatbusters :- why did you multiply with 2!?
Re: A traffic signal has 4 colors: Red, Blue, Green, and Yellow. Signals   [#permalink] 29 May 2019, 09:59
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