In a certain lottery, 7 balls are drawn at random from $n$ balls numbered from 1 to $n.$ If the probability that no pair of consecutive numbers is drawn is equal to the probability of drawing exactly one pair of consecutive numbers, and both probabilities are nonzero, then determine $n.$
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In a certain lottery, 7 balls are drawn at random from $n$ balls numbered from 1 to $n.$ If the prob...
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