The Olympic flag consists of five intertwined circles, one in each of the colors black, blue, green, red, and yellow. What is the probability that a random coloring of the five circles using these colors will produce the exact match of the Olympic symbol?
A) 1/5
B) 1/3125
C) 5/120
D) 1/120

Question

Quizplus · Accepted Answer

There are 5 choices for the color of the first circle, 4 choices for the color of the second circle (since it can't be the same as the first), 3 choices for the third circle, 2 choices for the fourth circle, and only 1 choice for the fifth circle. Therefore, there are $5 	imes 4 	imes 3 	imes 2 	imes 1 = 120$ possible colorings of the circles. Only one of these will be an exact match for the Olympic symbol, so the probability is $\frac{1}{120}$.

The Olympic Flag Consists of Five Intertwined Circles, One in Each