In a group of 21 aliens, there are 6 Cybermen, 7 Daleks and 8 Jovians.
(a) Suppose that 5 aliens are randomly chosen without replacement. Find the probability that at most 2 Cybermen are chosen.
(b) Suppose that 4 aliens are randomly chosen without replacement and it is known that 2 Cybermen are chosen. Find the probability that at least 1 Dalek is chosen.
(c) Suppose that 4 aliens are randomly chosen without replacement and it is known that at least 2 Daleks are chosen. Find the probability that no Jovian is chosen.
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