Question

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

Answer 1

`(5)/(14)`

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

=
`(C_3^2*C_6^4)/(C_9^4)`

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

=
`(5)/(14)`

Hence,

the correct answer is option (B) 5/14