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Updated on: 13 Aug 2018, 07:45
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.
Last edited by EgmatQuantExpert on 13 Aug 2018, 07:45, edited 7 times in total.
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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
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
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.
Answer D
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
04 Apr 2018, 20:33
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EgmatQuantExpert
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
PermutationA 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
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
