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A lotto problem (§4.2.3)
In each drawing of Lotto 6/45, six distinct numbers are drawn from the numbers 1,..., 45. In an analysis of 30 such lotto drawings, it was apparent that some numbers were never drawn. This is surprising. In total, 30 × 6 = 180 numbers were drawn, and it was expected that each of the 45 numbers would be chosen about four times. The question arises as to whether the lotto numbers were drawn according to the rules, and whether there may be some cheating occurring. What is the probability that, in 30 drawings, at least one of the numbers 1,..., 45 will not be drawn?
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