On April 24, 1980, the winning Pennsylvania daily number was 666. It was later discovered that on that day the drawing had been fixed by injecting a liquid into all balls except the 4 and the 6, assuring that only those numbers would appear as digits in the winning number. Interestingly, several weeks later the Pennsylvania lottery scandal was exposed, and within hours of the announcement of the lottery fix in Pennsylvania the winning number in the Connecticut lottery was 666. This coincidence was highly suspicious, but investigation of the Connecticut drawing concluded that its 666 drawing was legitimate
(a) Find the probability that 666 wins in a fair lottery-like the one in Connecticut.
(b) List all the possible outcomes for the Pennsylvania lottery on the day it was fixed.
(c) Find the probability that 666 would win in the fixed Pennsylvania lottery of April 24, 1980.
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