Probability exercise about allocating bottles of wine The exercise states the following: We have 15 bottles of wine that we will randomly distribute among three customers: A will get 2, B will get 8 and C will get 5. We've learned later that 4 of this 15 bottles are corked: _what are the chances that customer B doesn't get a single corked bottle of wine?_ I'm really having problems facing this kind of problem in which we use permutations and combinations to find the probability of an event. That's why I'd be thankful if someone presents me **multiple methods to solve this exercise** and explains me the intuition behind each one. Moreover, I'd appreciate to be explained **what kind of probability distribution it follows** , because I think it might follow a binomial distribution but I'm not able to present the problem in such terms.

The probability distribution involved here is the hypergeometric one.

The probability that customer B did only get bottles of wine that were not corked equals:$$\frac{\binom{11}{8}\binom{4}{0}}{\binom{15}{8}}=\frac{\binom{11}{8}}{\binom{15}{8}}$$

For a more direct way to calculate this probability see the answer of Ross.