A six-sided fair die is rolled six times independently. If side i is observed on the ith roll, it is called a match on the ith trial, i = 1, 2, 3, 4, 5, 6. Find the probabilities that
(a) all six trials result in matches,
(b) at least one match occurs in these six trials,
(c) exactly two matches occur in these six trials.
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