Note     : Whenever you use a formula, please detail in sentences exactly how/why it works for your particular solution (merely plugging values into a formula does not by itself demonstrate understanding). Proving a more general case of the formula(e) is another valid strategy.

Question: A box contains 4 red balls, 5 blue balls and 6 green balls. Five balls are removed from the box, at random. (In your solutions to the following questions, please use appropriate notations and/or words to justify all values that are given as part of your solutions.)

please solve all parts of above question

(a) What is the probability that at most one of the removed balls is red? [5] (b) What is the probability that the removed balls contain at least one ball of each of the three colours? [5] (c) Find the expectation and variance for the number of green balls among those removed. [10]