Bunuel wrote:
In a clothing store, there are six different colored neckties (red, orange, yellow, green, blue, and indigo) and six different colored shirts (red, orange, yellow, green, blue, and indigo) that must be packed into boxes for gifts. If each box can only fit one necktie and one shirt, what is the probability that all of the boxes will contain a necktie and a shirt of the same color?
A. 719/720
B. 1/120
C. 2/233
D. 3/543
E. 1/720
For the red necktie, there is a 1/6 chance it will be packed with the red shirt. Given that the reds have been packed together, for the orange necktie, there is a 1/5 chance it will be packed with the orange shirt. Given that the oranges have been packed together, for the yellow necktie, there is a 1/4 chance it will be packed with the yellow shirt. From this point, we see that there is a 1/3 chance the green necktie and shirt will be packed together, a 1/2 chance the blue necktie and shirt will be packed together and, finally, a 1/1 chance the indigo necktie and shirt will be packed together. Therefore, the overall probability is 1/6 x 1/5 x 1/4 x 1/3 x 1/2 x 1/1 = 1/6! = 1/720.
Answer: E
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