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

PermutationInitially, 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 arrangementsFundamental 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

_________________

In the depths of winter, I finally learned

that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"