Question: 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 shows if the order of the colors defines unique cases?

1. 3
2. 6
3. 8
4. 12
5. 24

Answer:
Solution with Explanation:
Approach Solution (1):

Signals can be generated by selecting 2 colors and rearranging them.
Out of 4 colors: Red, Blue, Green, and Yellow
2 can be selected in 4C2 ways = 6 ways
Arrangement = 2! = 2 ways
Number of signals = 6 * 2 = 12 ways

Correct Option: D

Approach Solution (2):

Using 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 fot the second choice.
Therefore, 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

Correct Option: D

Approach Solution (3):

Given: A traffic light has signals of 4 colors: Red, Blue, Green and Yellow
The traffic light will show a signal by combining 2 of these e4 colors
To find: we need to find the number of ways in which 2 colors can be chosen out of 4 colors
Approach: Since the picking of 2 different colors gives a different signal, the ways of picking 2 colors are dependent on each other.
Hence, total ways to pick colors = number of ways to pick 1 color from 4 colors and number of ways to pick another color
Total ways = 4 * 3 = 12

Correct Option: D

“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 shows if the order of the colors defines unique cases?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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