At a blind taste competition a contestant is offered 3 cups of each of the 3 samples of tea in a random arrangement of 9 marked cups. If each contestant tastes 4 different cups of tea, what is the probability that a contestant does not taste all of the samples?	Answers: A) 1/12 B) 5/14 C) 4/9 D) 1/2 E) 2/3
"The probability that a contestant does not taste all of the samples" means that contestant tastes only 2 samples of tea (one sample is not possible as contestant tastes 4 cups&gt;3 of each kind).   C23∗C46C49=514C32∗C64C94=514.   C23C32 - # of ways to choose which 2 samples will be tasted;   C46C64 - # of ways to choose 4 cups out of 6 cups of two samples (2 samples*3 cups each = 6 cups);   C49C94 - total # of ways to choose 4 cups out of 9.   Answer: 5/14
<result>B</result>
At a blind taste competition a contestant is offered 3 cups of each of the 3 samples of tea in a random arrangement of 9 marked cups. If each contestant tastes 4 different cups of tea, what is the probability that a contestant does not taste all of the samples?