An I.R.S auditor will inspect 5 of 12 tax returns, out of which 6 contain illegitimate deductions. Suppose he chooses the returns randomly.
(a) Determine the probability that he catches exactly 3 illegitimate deductions.
(b) Determine the probability that he catches at least 2 illegitimate deductions.
(c) Determine the standard deviation of the number of illegitimate deductions he will catch.