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? a. 1/12b. 5/14c. 4/9d. 1/2e. 2/3

Step-by-step explanation:

Data provided in the question:

Number of cups of tea offered = 3

Number of cups marked = 9

Number of cups tasted by each = 4

Now,

The probability that a contestant does not taste all of the samples

= contestant tastes only 2 samples of tea

=

C₆⁴ = number of ways to choose 4 cups out of 6 cups of two samples

C₃² = number of ways to choose which 2 samples will be tasted

[ as 2 samples × 3 cups each = 6 cups ]

C₉⁴ = Number of ways to choose 4 cups out of 9

=

Hence,

the correct answer is option (B) 5/14

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step-by-step explanation: