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

Question

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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generis · Accepted Answer

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

Answer D

GMATBusters · Answer

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.

Answer D

EgmatQuantExpert · Answer

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.
 
  Answer: D

Manat · Answer

gmatbusters  :- why did you multiply with 2!?

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

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